delivered the opinion of the court:
Defendant Mark Secor was convicted of one count of criminal sexual assault (720 ILCS 5/12 — 13(a)(4) (West 1994)) and one count of aggravated criminal sexual abuse (720 ILCS 5/12 — 16(d) (West 1994)) and he was sentenced to concurrent terms of six and three years’ imprisonment. On appeal defendant contends that: (1) the State failed to prove him guilty of criminal sexual assault beyond a reasonable doubt; (2) section 12 — 13(a)(4) of the Criminal Code of 1961 (the Code) is unconstitutionally vague; and (3) defendant was denied a fair trial by the State’s opening statement. We affirm.
The 14-year-old victim, J.L., testified that on December 21, 1994, he and his 11-year-old brother, Peter, spent the night at the defendant’s house visiting the defendant’s son, Gregg. J.L. had been in the house "[a] lot” and he had spent the night there "a couple” of times before. When J.L. and Peter arrived at approximately 6:30 p.m., the defendant was not present. The three boys played video games for about an hour in Gregg’s room. The defendant then drove them to a video store and to a gas station. They were gone approximately one hour. After returning, the boys again played video games until 11 p.m., when the defendant told them to go to bed. J.L. slept on the bed in Gregg’s room; Peter and Gregg slept on the floor a few feet from J.L. J.L. awoke during the night and saw the defendant sitting on the bed next to him. The defendant had his hand on J.L.’s thigh. The defendant told J.L. that he was covering him up, and he pulled the covers over him and left. J.L. testified that subsequently, on three separate occasions, the defendant came into the room and fondled and placed his mouth on J.L.’s penis. The next evening, J.L. told his mother what had happened and the defendant was later arrested. According to J.L., he saw the defendant two days after the incident. The defendant asked J.L. if he had gotten him a Christmas present and if he had slept well that night.
*392On cross-examination, J.L. admitted that he could have gone home if he had wanted to and that the defendant had not prevented him from leaving. J.L. acknowledged that the idea of sleeping over at the defendant’s house originated with the three boys, not with the defendant. On redirect examination, J.L. stated that he did not leave the defendant’s house because he was scared and did not know what to do.
J.L.’s mother, P.L., testified that she and her family had known the defendant and his family for 10 years. Prior to the night of the incident, her children had spent the night at the defendant’s house approximately six times. In addition, the defendant’s children had spent about the same number of nights at P.L.’s house. P.L. stated that she had given permission for J.L. and his brother to spend the night at the defendant’s house. On that same night, the defendant’s daughter was staying overnight at P.L.’s house, visiting P.L.’s daughter. According to P.L., the two families had exchanged children in this manner before.
Richard Demick, an investigator for the Joliet police department, testified that he interviewed the defendant on January 18, 1995. The defendant initially denied committing the offenses, but later admitted fondling and placing his mouth on J.L.’s penis.
The State rested its case and the defendant’s motion for a directed verdict and motion to dismiss were denied. The defendant chose not to present any evidence and, as indicated above, the jury found the defendant guilty of criminal sexual assault and aggravated criminal sexual abuse.
The defendant first contends that the State failed to prove him guilty beyond a reasonable doubt of criminal sexual assault. Specifically, defendant maintains that the State completely failed to produce any evidence that he occupied a position of trust or supervision in relation to the victim. We disagree.
Section 12 — 13 of the Code provides in part:
"The accused commits criminal sexual assault if he or she:
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(4) commits an act of sexual penetration with a victim who was at least 13 years of age but under 18 years of age when the act was committed and the accused was 17 years of age or over and held a position of trust, authority or supervision in relation to the victim.” 720 ILCS 5/12 — 13(a)(4) (West 1994).
The defendant argues that he was convicted of violating this section on the basis of the victim’s mere presence in his home. The defendant maintains that section 12 — 13(a)(4) was intended to apply only where an offender exploits his relationship with the child to fa*393cilitate the commission of the offense. Defendant asserts that it is only the systematic, predatory and deliberate use of one’s position to abuse children that the legislature intended to prevent.
In People v. Kaminski, 246 Ill. App. 3d 77, 615 N.E.2d 808 (1993), the 17-year-old victim spent the night at the home of her sister, Roberta, and Roberta’s husband, the defendant. The victim had known the defendant for a little more than a year. The victim had obtained permission from her parents and Roberta for the overnight stay, and the victim’s father testified that Roberta and the defendant were responsible for the victim that night. After socializing with her sister, the defendant, and another couple, the victim went to sleep on a sofa bed in the living room. Some time later the defendant sexually assaulted her. Evidence was presented that the defendant told police that during the night he heard the victim coughing, so he placed a blanket on her and turned up the heat. The trial court found that the defendant held a position of supervision with respect to the victim.
On appeal, the defendant argued that the evidence established that he was merely a "one-time over-night host” and that section 12-13(a)(4) of the Code was inapplicable as that section was designed to prevent individuals from exerting undue influence over a child. The court stated:
"The ability of individuals who hold positions of supervision to exert undue influence over a child is certainly a relevant factor. While we agree that this is one purpose served by the statute, we also recognize that it is the position of 'trust, authority or supervision’ which often provides a heightened opportunity for the sexual assault to occur. For example, a baby-sitter or camp counselor might be able to assault sexually a child under his or her supervision primarily because of the opportunity that position provides rather than because of any 'undue influence’ which is exerted over the child. The vulnerability of a child in such circumstances is a separate factor which justifies the stronger penalty provided under section 12 — 13(a)(4). Moreover, it is not unreasonable to consider the possibility that, in certain instances, increased emotional trauma may result from an assault perpetrated by one who has been entrusted to occupy a position of supervision over a child.” Kaminski, 246 Ill. App. 3d at 81, 615 N.E.2d at 811.
The Kaminski court went on to find that there was sufficient evidence that the defendant held a position of supervision in relation to the victim. The court stated that the phrase "position of supervision” included situations in which an individual is an overseer, caretaker or chaperone of a child. The court concluded that, considering all the facts and circumstances, the defendant and his wife were responsible *394for the victim’s welfare on the night of the assault. The court specifically noted that the defendant would not have had the opportunity to assault the victim had her parents not entrusted her care to the defendant and his wife that night.
We find that the evidence of trust or supervision in this case is stronger than that presented in Kaminski. The defendant emphasizes the Kaminski court’s reliance on the existence of a family relationship between the victim and the defendant. While the defendant and the victim in this case are not related, we nevertheless believe that their relationship raises a strong inference of trust and supervision. Thé nature of defendant’s function in that relationship could be characterized, at a minimum, as that of baby sitter or chaperone. Whether or not the defendant was initially aware of the boys’ plans to sleep over, he clearly accepted the role of chaperone by driving them to the video store and telling them to go to bed. Contrary to defendant’s claim that these are "insignificant occurrences,” we find that they are strongly suggestive of defendant’s assumption of a parental or quasi-parental role. In addition, we cannot ignore the fact that the families of the defendant and the victim had been friends for 10 years, a circumstance likely to generate mutual trust. This trust was demonstrated on the occasions when the children slept at each others’ houses.
Defendant’s argument that application of section 12 — 13(a)(4) to him is based merely on his status as an adult is not well taken. J.L. was not a stranger to the defendant; he was the child of neighbors of long standing and a friend of his son. Moreover, the circumstances of the crime suggest that defendant was aware of his influence over J.L. Defendant committed the sexual acts while J.L.’s brother and the defendant’s own son slept on the floor a few feet away. It would not have been unreasonable for the jury to infer that defendant was relying on his position of trust, authority or supervision as assurance that J.L. would not cry out.
When presented with a challenge to the sufficiency of the evidence, the relevant question on review is whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime proved beyond a reasonable doubt. People v. Havre, 155 Ill. 2d 392, 614 N.E.2d 1235 (1993); People v. Collins, 106 Ill. 2d 237, 478 N.E.2d 267 (1985). We find that the jury’s determination that defendant was in a position of trust, authority or supervision in relation to the victim was supported by the evidence.
Defendant also argues that section 12 — 13(a)(4) is unconstitutionally vague, resulting in a denial of due process. Defendant *395maintains that the phrase "held a position of trust, authority or supervision” (720 ILCS 5/12 — 13(a)(4) (West 1994)) is so vague and undefined that it leaves enforcement of the law to the whim of the arresting officer, judge or jury. We disagree.
Due process requires that the proscription of a penal statute must be clearly defined. People v. Taylor, 138 Ill. 2d 204, 561 N.E.2d 667 (1990); People v. Haywood, 118 Ill. 2d 263, 515 N.E.2d 45 (1987). This requirement furthers three important policies: (1) it gives a person of ordinary intelligence a reasonable opportunity to know what is prohibited so that he may conform his conduct to the requirements of the law; (2) it provides standards which serve to prevent the arbitrary or discriminatory application of the law by police, judges or juries; and (3) where first amendment rights are implicated, it insulates the exercise of those rights from the chilling effect created by fear that such conduct may fall within the statute’s prohibitions. Taylor, 138 Ill. 2d 204, 561 N.E.2d 667.
When a statute which does not involve first amendment rights is challenged as unconstitutionally vague on its face, it will be invalidated only if no standard of conduct at all is specified. Taylor, 138 Ill. 2d 204, 561 N.E.2d 667. In other words, to sustain a facial challenge, the defendant must demonstrate that the law is incapable of any valid application. Haywood, 118 Ill. 2d 263, 515 N.E.2d 45.
In this case the defendant does not contend that section 12— 13(a)(4) infringes upon any right protected by the first amendment, nor do we discern any such infringement. In addition, while defendant at one point appears to challenge the validity of the statute on its face, he admits in his brief that "[i]ts application in some circumstances is unquestioned.” Those circumstances would include, we believe, baby sitters, teachers, day-care workers, priests and ministers, scout .leaders and a host of other positions of trust, authority or supervision. We find, therefore, that section 12 — 13(a)(4) is not facially invalid.
We next consider whether section 12 — 13(a)(4) is unconstitutionally vague as applied to the defendant in this case. Defendant claims that the statute fails to give fair notice of what conduct is prohibited and provides no standards to guide police, judges and juries in determining when the statute is violated. Defendant argues that "[wjhen and whether a defendant occupies a position of trust, authority or supervision is left to the uninstructed emotions of individual prosecutors and juries.”
Due process does not require impossible levels of specificity; instead, a statute must convey sufficiently definite warnings that can be understood when measured by common understanding and *396practice. Taylor, 138 Ill. 2d 204, 561 N.E.2d 667; Haywood, 118 Ill. 2d 263, 515 N.E.2d 45. Statutes enjoy a presumption of constitutionality (People v. Caffrey, 97 Ill. 2d 526, 455 N.E.2d 60 (1983)) and should be construed so as to affirm their constitutionality and validity if it can reasonably be done (Haywood, 118 Ill. 2d 263, 515 N.E.2d 45). Words used in a statute are presumed to have their ordinary and popularly understood meanings. Caffrey, 97 Ill. 2d 526, 455 N.E.2d 60.
The term "trust” is defined as "[cjonfidence in the integrity, ability, character, and truth of a person ***[;] [something committed into the care of another.” American Heritage Dictionary 1300 (2d coll. ed. 1985). "Authority” is "[t]he power to command, enforce laws, exact obedience, determine, or judge.” American Heritage Dictionary 142 (2d coll. ed. 1985). "Supervise” or "supervision” means "[t]o direct and inspect the performance of’ (American Heritage Dictionary 1221 (2d coll. ed. 1985)); the act of overseeing or inspection (City of Geneseo v. Illinois Northern Utilities Co., 378 Ill. 506, 39 N.E.2d 26 (1941)); to superintend or oversee (Kaminski, 246 Ill. App. 3d 77, 615 N.E.2d 808).
We believe that the terms "trust,” "authority” and "supervision” are sufficiently definite to both warn potential defendants of the type of conduct that is prohibited and to channel the discretion of police, judges and juries. While these terms admittedly contain some measure of ambiguity, "we can never expect mathematical certainty from our language” (Grayned v. City of Rockford, 408 U.S. 104, 110, 33 L. Ed. 2d 222, 228-29, 92 S. Ct. 2294, 2300 (1972)). It is evident that, in enacting section 12 — 13(a)(4), the legislature sought to prevent sex offenses by those whom a child would tend to obey, such as a teacher or coach, as well as those in whom the child has placed his trust, such as the defendant. It is the trust that makes the child particularly vulnerable, and it is the betrayal of that trust that makes the offense particularly devastating. Due process does not require a "laundry list” of all such positions of trust, authority or supervision; where enumeration of all such positions is impractical, the legislature may reasonably choose sufficiently broad language to encompass such situations. See People v. Khan, 136 Ill. App. 3d 754, 483 N.E.2d 1030 (1985). We need not, of course, consider whether the statute might be vague as applied to some hypothetical situation. "A defendant may be prosecuted under a statute without violating his right of due process if his conduct falls squarely within the statute’s proscription, even though the statute may be vague as applied to other conduct.” Taylor, 138 Ill. 2d at 211, 561 N.E.2d at 670. As we determined above, the defendant was clearly in a position of trust or supervision in relation to J.L. We find that section 12 — 13(a)(4) is not unconstitutionally vague as applied.
*397Finally, the defendant contends that he was deprived of a fair trial when the prosecutor told the jury during his opening statement that he would introduce evidence that on the day before the incident, .the defendant called P.L. and "personally asked if it was okay for her sons to spend the night at the Secor residence.” The defendant moved for a mistrial based on the State’s failure to disclose the alleged statement during discovery. The State admitted that the statement had not been disclosed, and the trial court found that a discovery violation had occurred. The court refused the defendant’s request for a mistrial, however, and instead prohibited the State from presenting any evidence regarding the alleged telephone call. The court also offered to admonish the jury concerning the statement, but the defendant declined. Defendant now maintains that he was severely prejudiced by introduction of the alleged statement, which he contends improperly bolstered the State’s claim that he sought and accepted a position of trust and supervision in relation to J.L. The defendant argues that the State’s use of the undisclosed statement was "tantamount to alleging a confession” to the charge of criminal sexual assault and denied him a fair trial.
Supreme Court Rule 412 requires the State to disclose to defense counsel the substance of any oral statements made by the defendant and a list of witnesses to the making of such statements. 134 Ill. 2d R. 412. The purpose of the rule is to protect a defendant against surprise, unfairness and inadequate preparation, and to afford the defense an opportunity to investigate the circumstances surrounding the statement. People v. Pasch, 152 Ill. 2d 133, 604 N.E.2d 294 (1992); People v. Cisewski, 118 Ill. 2d 163, 514 N.E.2d 970 (1987). The failure to comply with Rule 412 does not always require a new trial; a new trial should only be granted if the defendant was prejudiced by the discovery violation and the trial court failed to eliminate the prejudice. Cisewski, 118 Ill. 2d 163, 514 N.E.2d 970; People v. Siefke, 195 Ill. App. 3d 135, 551 N.E.2d 1361 (1990). Among the factors to be considered in determining whether the defendant is entitled to a new trial are the closeness of the evidence, the strength of the undisclosed evidence, the likelihood that prior notice would have helped the defense discredit the evidence, and the willfulness of the State in failing to disclose the evidence. People v. Robinson, 157 Ill. 2d 68, 623 N.E.2d 352 (1993); Siefke, 195 Ill. App. 3d 135, 551 N.E.2d 1361.
In this case, although a discovery violation clearly occurred, we do not believe that the defendant was prejudiced to the extent that a new trial is required. While the allegation that the defendant telephoned the victim’s mother and requested permission for the sleepover may have been improperly considered by the jury as ad*398ditional evidence of the defendant’s position of trust, authority or supervision, there was ample admissible evidence to sustain defendant’s conviction. As we noted above, whether or not the defendant was initially aware of the boys’ plans to sleep over, he clearly, accepted the role of chaperone by taking the boys to the video store and telling them to go to bed. Defendant’s actions implicitly sanctioned the sleepover and signaled his acceptance of responsibility for the boys’ welfare. Perhaps more significant was the mutual trust developed between the two families over time, as evidenced by the prior overnight exchanges of children. In view of this evidence, we believe that the jury’s verdict would have been the same even if the alleged phone call had not been mentioned. We also note that, prior to opening statements, the trial judge informed the jury that opening statements are not evidence and were not to be considered as evidence, as did the assistant State’s Attorney. The jury also received an instruction to the same effect. These admonitions diminished any prejudicial effect caused by reference to the alleged telephone call.
For the reasons stated above, the judgment of the circuit court is affirmed.
Affirmed.
LYTTON and McCUSKEY, JJ„ concur.