GRILLO, J.

The defendant pleaded guilty to criminal charges arising out of facts revealed by the bill of particulars and the statements made by the parties at the time of the plea, which are as follows: On or about January 26, 1981, the victim's mother entrusted the care of her two year old daughter to her live-in boyfriend, the defendant George Eason. When the mother returned home from her job at a nursing home, she noticed that her child's face was scratched and her lip was bruised and swollen. She questioned the defendant about her daughter, and he stated that the child had fallen down some stairs. That same evening, the mother again left her child with the defendant while she worked her second job from 8 p.m. until midnight. When the mother returned home after work, she found blood on a cloth with which she was washing her daughter's vaginal area after the child used the bathroom.

A medical examination at Waterbury Hospital revealed bruises on the front of the child's thighs and stomach, as well as cuts on her right side and stomach. The outside of the child's vagina was red and swollen; there were also bruises on the inside of her vagina. The hymen was found intact. The medical report stated: "FINAL DIAGNOSIS: 1. Child abuse. Possible sexual assault." The defendant was located and questioned by a member of the Waterbury police department the following day. After he admitted verbally that he had hit the child with a belt, he was arrested and charged in connection with the child's injuries.

On March 8, 1982, after plea negotiations, the state filed a bill of particulars and a substitute information charging the defendant in the first count with the crime of injury or risk of injury to, or impairing the morals of, a child; General Statutes 53-21; and in the second count with the crime of sexual assault in the fourth degree; General Statutes 53a-73a (a)(1). The defendant was sentenced to a prison term of not less than two nor more than four years following his guilty plea to a charge of injury or risk of injury to, or impairing the morals of, a child under 53-21. The defendant's motion to dismiss challenging the constitutionality of 53-21, first made prior to the entry of his plea and later renewed, was denied immediately prior to the imposition of his sentence. On May 11, 1982, the court filed a memorandum of decision on the defendant's motion to dismiss. On May 28, the defendant appealed to this court from the denial of his motion to dismiss.

The two issues presented to us in this appeal are (1) whether an erroneous finding that the defendant "admitted that he intentionally subjected the child to sexual contact" vitiates his guilty plea to a violation of 53-21 based upon an information charging both an impairment of the health as well as the morals of a child, and (2) whether 53-21 as applied to the facts of this case is unconstitutionally vague so as to violate the defendant's due process rights.

At the outset, it is necessary to outline the precise crimes with which the defendant was charged and to which he pleaded guilty. Count one of the substitute information charged the defendant with "the crime of Injury or Risk of Injury to, or Impairing the morals of, a child, in violation of Section 53-21 of the General Statutes." The bill of particulars charged that the defendant "beat this baby about the head and body with, among other things, a belt. He also intentionally subjected this baby to sexual contact."

We note that the substitute information employs the alternative or disjunctive "or" while the bill of particulars employs the conjunctive "also." The substitute information in this case is improperly drafted since "[a]n information which charges the commission of two or more offenses in the alternative is fatally defective for the reason that it does not definitely apprise the accused of the specific charge against him. Though the statute makes criminal the commission of several acts stated disjunctively, the information must charge in the conjunctive since otherwise it would be uncertain which of two or more accusations was intended." Grasso v. Frattolillo, 111 Conn. 209, 212, 149 A. 838 (1930); see also State v. Cofone, 164 Conn. 162, 167, 319 A.2d 381 (1972). In this case, however, the faulty substitute information is remedied by the bill of particulars, which sets out the charges in the conjunctive. "`The office of a bill of particulars is to supply both the accused and the court additional information concerning an accusation that the defendant has committed an act or acts constituting a criminal offense.'" State v. Coleman, 167 Conn. 260, 269, 355 A.2d 11 (1974), quoting 41 Am Jur. 2d, Indictments and Informations 163. Therefore, since the substitute information and the bill of particulars are read together, it is clear that the defendant was charged with two criminal acts violative of 53-21: (1) doing an act likely to impair the health of a child (beating with a belt) and (2) doing an act likely to impair the morals of a child (subjecting to sexual contact). The defendant maintains that the facts which he admitted when he pleaded guilty did not include the allegation that he had had sexual contact with the child. Rather, the defendant claims that he understood the recitation of facts to involve only that portion of the statute concerning endangerment to the health of the child. Succinctly stated, the defendant states that he pleaded guilty only to beating the child with a belt (endangering her "health"), and that he did not plead guilty to any sexual contact ("impairing her morals"). Since the defendant was charged under 53-21, a criminal statute embodying several alternative acts, his claim is without merit even if his contention that he admitted only to the beating of the child is correct.

In State v. Cofone, supra, 168, we held that where an information alleges a crime to have been committed in more than one way, a guilty finding stands if the evidence would support a conviction based upon any one of the statutory alternatives. In this case, even though we find nothing in the transcript to indicate that the defendant admitted to anything more than beating the child with a belt, his plea must stand. Since the defendant was charged with committing an act likely to impair the health and an act likely to impair the morals of a child, the uncontested fact that the defendant beat the child with a belt adequately supported the judgment of guilty in violation of 53-21 even if the trial court's finding of an impairment of morals is disregarded. The erroneous finding in the memorandum of decision was a harmless error insofar as the validity of the guilty plea was concerned. See North Carolina v. Alford, 400 U.S. 25, 91 S.Ct. 160, 27 L.Ed.2d 162 (1970).

The defendant also argues that since there was confusion in his mind as to the portion of the statute to which he was pleading guilty, his plea was not knowing, voluntary and intelligent, and it was in violation of Practice Book 711. In order for a plea of guilty to be constitutionally valid, the record must affirmatively disclose that there is a factual basis for the plea and that the defendant entered the plea voluntarily and intelligently. Practice Book 710-713; State v. Childree, 189 Conn. 114, 119, 454 A.2d 1274 (1983); Blue v. Robinson, 173 Conn. 360, 373, 377 A.2d 1108 (1977). "`[I]f a defendant's guilty plea is not equally voluntary and knowing, it has been obtained in violation of due process and is therefore void.' McCarthy v. United States, [ 394 U.S. 459, 466, 89 S.Ct. 1166, 22 L.Ed.2d 418 (1969)]." State v. Battle, 170 Conn. 469, 473, 365 A.2d 1100 (1976).

The defendant's claim that his plea was not intelligent and, therefore, that it was involuntary is unsound. "Unless the defendant has had real notice of the nature of the charge against him, the plea cannot constitute an intelligent admission." State v. Marra, 174 Conn. 338, 340, 387 A.2d 550 (1978), quoting Henderson v. Morgan, 426 U.S. 637, 645, 96 S.Ct. 2253, 49 L.Ed.2d 108 (1976). The plea must also be supported by a factual basis. State v. Battle, supra, 473. Such a factual basis is absent when the recited facts reveal less than all the elements of the crime charged. Id., 472. A reading of the state's attorney's presentation of the facts in the present case; see footnote 6, supra; reveals that the defendant had "real notice" of the nature of the charge. The recitation contains facts pertinent to the charge of impairment to health (hitting with a belt), as well as to the charge of impairment to morals (sexual contact). These facts were recited to the defendant at the plea hearing and include all of the elements to support a charge of risk of injury as set out in State v. Martin, 189 Conn. 1, 7-8, 454 A.2d 256 (1983): "(1) that the victim was less than sixteen years old; (2) that the defendant had perpetrated an act upon the victim; (3) that this act was likely to be injurious to his health; and (4) that the defendant had a general criminal intent to perform such act." The defendant also indicated that the facts were substantially correct. Furthermore, we may presume that the nature of the plea proceedings and all documents, such as the bill of particulars and medical reports, were explained to the defendant by his counsel. As we noted in State v. Torres, 182 Conn. 176, 184, 438 A.2d 46 (1980): "[T]he court was entitled to presume that `defense counsel routinely explain the nature of the offense in sufficient detail to give the accused notice of what he is being asked to admit.' Henderson v. Morgan, 426 U.S. 637, 647, 96 S.Ct. 2253, 49 L.Ed.2d 108 (1976); Blue v. Robinson, 173 Conn. 360, 375-76, 377 A.2d 1108 (1977). Except for those inquiries which are constitutionally mandated or are required by our rules; Practice Book, 1978, 711-713; the court is not obliged to assume the role of the defendant's counselor."

Lastly, the 711 requirement of an adequate factual basis is also satisfied by the transcript of the plea hearing. The defendant was fully apprised of the nature of the charge, of the maximum sentence, and of the panoply of constitutional rights of which he could avail himself. Therefore, we find that the lower court properly accepted the guilty plea of the defendant.

We now turn to the defendant's second argument, that the section of 53-21 which deals with impairment of health is so vague as to violate the due process provisions of both article first, 8 of the state constitution and the fourteenth amendment to the federal constitution. He submits that in order to survive a vagueness challenge, a statute must (1) give fair notice or warning that the conduct is proscribed, and (2) establish reasonable guidelines for law enforcement officials and triers of fact in order to prevent arbitrary and discriminatory enforcement. The defendant argues that 53-21 fails to comply with this two-part test.

This court, in State v. Pickering, 180 Conn. 54, 428 A.2d 322 (1980), recently set out the basic principles to be considered when a statute is attacked as void for vagueness. First, the constitutionality of the challenged statute is to be determined by the statute's applicability to the particular facts at issue. Id., 57. "[T]hat a statutory provision may be of questionable applicability in speculative situations is usually immaterial if the challenged provision applies to the conduct of the defendant in the case at issue." Id., 58. Second, the statute must give fair warning in order to enable a person to know what conduct he must avoid. "[A] statute which either forbids or requires the doing of an act in terms so vague that men of common intelligence must necessarily guess at its meaning and differ as to its application violates the first essential of due process of law." Id., 60, quoting Connally v. General Construction Co., 269 U.S. 385, 391, 46 S.Ct. 126, 70 L.Ed. 322 (1926). "Thus, a penal statute may survive a vagueness attack solely upon a consideration of whether it provides fair warning." Id., 61. "References to judicial opinions involving the statute, the common law, legal dictionaries, or treatises may be necessary to ascertain the statute's meaning to determine if it gives fair warning." Id., 62-63, citing Rose v. Locke, 423 U.S. 48, 49-50, 96 S.Ct. 243, 46 L.Ed.2d 185 (1975).

Black's Law Dictionary defines "health" as the "state of being hale, sound, or whole in body, mind or soul or well being. Freedom from pain or sickness." Black's Law Dictionary (5th Ed. 1979). The words "act likely to impair the health of a child" have also been elucidated through several opinions of this court. In State v. Palozie, 165 Conn. 288, 292, 334 A.2d 468 (1973), we found that each of three separate acts would be sufficient to convict the defendant of an act likely to impair a child's health: (1) "[s]trapping a child to a degree that bruises with some scabbing covering an area of three or four inches result and further causing a two-to-three-inch area to become black and blue, "(2) "throwing a child against a chair, bruising his head, and then stepping on his back, which caused vomiting that night and the next day," or (3) "slapping his son and then `poking' his son in the nose." In State v. Martin, 189 Conn. 1, 6, 454 A.2d 256 (1983), we found that the defendant's act of pushing a child "into a wall and then to the floor" which caused the child to sustain "a bloody nose, a split lip, a lump on his head, facial bruises, and red marks on his arm" was violative of that portion of 53-21 dealing with acts likely to impair a child's health. In addition, in State v. Dennis, 150 Conn. 245, 188 A.2d 65 (1963), this court further defined acts violative of this latter portion of the risk of injury statute as "acts directly perpetrated on the person of a minor and injurious to his moral or physical well-being. "Id., 250.

It is not necessary that this statute list the precise actions prohibited by it. Penal laws may be general and prohibit a wide range of conduct; the constitution requires no more than reasonableness of certainty. State v. Chetcuti, 173 Conn. 165, 167, 377 A.2d 263 (1977), citing United States v. Petrillo, 332 U.S. 1, 7-8, 67 S.Ct. 1538, 91 L.Ed. 1877 (1942). This court's opinions pursuant to 53-21 make it clear that an act injurious to the physical well-being of a child is prohibited. These cases give fair warning that the defendant's act of hitting a child with a belt was proscribed at the time he committed the act. "This is not a situation where the state is holding an individual `criminally responsible for conduct he could not reasonably understand to be proscribed.' United States v. Harriss, [ 347 U.S. 612, 617, 74 S.Ct. 808, 98 L.Ed. 989 (1954).] On the contrary, this is an instance where the statute `as authoritatively construed [applies] without question to certain activities.' Smith v. Goguen, [ 415 U.S. 566, 578, 94 S.Ct. 1242, 39 L.Ed.2d 605 (1974).]" State v. Pickering, supra, 64-65. Considered in light of the defendant's opprobrious conduct, the statutory language is not vague as applied in this case.

Lastly, the defendant argues that the principle of lenity should be employed to decrease his sentence to one year or less. This claim of lenity, however, was not raised by the defendant when he entered his guilty plea on March 8, 1982. At no time during the sentencing hearing did defense counsel raise the lenity claim. The lower court's written memorandum of May 11, 1982, makes no mention of lenity. We are not bound to consider questions not raised at trial by a defendant even in a criminal case. State v. Williams, 173 Conn. 545, 560, 378 A.2d 588 (1977).