
80 Ill. App.3d 535 (1980)
400 N.E.2d 511
THE PEOPLE OF THE STATE OF ILLINOIS, Plaintiff-Appellee,
v.
RONALD BRISTOW, Defendant-Appellant.
Nos. 79-35, 79-36 cons.
Illinois Appellate Court  First District (4th Division).
Opinion filed January 24, 1980.
*536 Richard E. Zulkey, of Zulkey, Pikarski & Gottlick, and John P. Coleman, of O'Brien & Coleman, both of Chicago, for appellant.
Bernard Carey, State's Attorney, of Chicago (Marcia B. Orr and Wesley H.H. Ching, Assistant State's Attorneys, of counsel), for the People.
Reversed and remanded in 79-35; Judgment vacated in 79-36.
Mr. JUSTICE ROMITI delivered the opinion of the court:
Following a bench trial, the defendant, Ronald Bristow, was found guilty of criminal damage to property (Ill. Rev. Stat. 1977, ch. 38, par. 21-1(a)), and sentenced to a term of 60 days in the House of Correction. Several months later he filed a petition pursuant to section 72 of the Civil Practice Act (Ill. Rev. Stat. 1977, ch. 110, par. 72), to set aside the judgment based on the existence of an additional witness favorable to his defense. The petition was denied. Defendant has appealed from the judgment of conviction (Docket No. 79-35), and the judgment on his section 72 petition (Docket No. 79-36). The two cases have been consolidated for decision. In his direct appeal, defendant contends that he was denied his constitutional right to a trial by jury; he was not proved guilty beyond a reasonable doubt; he was denied due process by the restricted scope of the cross-examination of the complainant; and the trial court erred by denying his motion for a new trial.
Debra Keeling testified that on April 7, 1978, between 11:30 p.m. and 1 a.m., she was sitting in her living room at 4128 North Lawndale in Chicago. The room had seven windows across the front and it was illuminated because of a light from the street. She saw the defendant, Ronald Bristow, walk down the street toward her residence and stop. He had an object in his hand. She then saw a brick come through the window, shattering the glass which hit her desk. She did not see the defendant again. However, she reported the incident to the police around 8 a.m.
On cross-examination she admitted that over a year prior thereto she had lived with the defendant for a while, but that their relationship had been terminated for several months. She stated the defendant was not wearing a hat and that she had a good view of him on the night of the occurrence.
The defendant testified on his own behalf that he was with Sandy Mendyk in her home for dinner on April 7, 1978, and remained there until 6 a.m. He denied throwing a brick through the complainant's window. On cross-examination he admitted that he might have gone outside of the house to "tinker" with his bike or car on the night of the incident.
*537 Sandra Mendyk testified that the defendant was with her in her home at 6935 West Berwyn in Chicago on the night of April 7, 1978. She stated he came for dinner about 5 p.m. and did not leave until the next morning around 6 a.m. She admitted that she did not see him leave but remembered hearing him depart while she was sleeping.
The trial court entered a finding of guilty of criminal damage to property. Thereafter the defendant filed a written motion for a new trial in which he questioned the sufficiency of the evidence and also raised the issue of new and additional evidence. On the latter point defendant called Thomas Weldon, who testified that he threw a brick through the complainant's window because he was angry with her over her treatment of the defendant. On cross-examination, he stated he had known the defendant for 15 years and sometimes worked for the defendant. He also admitted that he told the defendant about his act the night after it happened, and the defendant told him not to worry about the incident. The trial court denied the motion for a new trial and sentenced the defendant.
Several months thereafter, defendant filed his section 72 petition (Ill. Rev. Stat. 1977, ch. 110, par. 72). Defendant asserted that he now had a witness, who was previously reluctant to testify, who would account for his whereabouts on the night of the occurrence. The motion was denied.

I.
Defendant first contends that his conviction must be reversed because the record does not show that he was admonished by the trial court of his right to a jury trial, and it fails to show that a waiver of jury was made. The State replies that the defendant has waived the jury trial issue by failing to raise it in his written motion for a new trial.
That following colloquy is essential to consideration of the jury waiver issue.
"THE COURT: * * * Swear in the witnesses.
(Witnesses sworn.)
THE COURT: Plea of not guilty?
MR. BROW [Defense counsel]: Yes, your Honor.
THE COURT: Jury waived?
MR. SALANT [Assistant State's Attorney]: I make a motion to exclude witnesses."
The record shows that defense counsel did not reply to the trial court's question as to whether a jury was waived, and that immediately thereafter the State made a motion to exclude witnesses and called its first witness.
 1, 2 A trial court has a duty to see that a defendant's waiver of the right *538 to trial by jury is expressly and understandingly made in open court. (People v. Banks (1979), 71 Ill. App.3d 15, 389 N.E.2d 180.) Here, there is no claim that the record is incomplete, and we must, therefore, conclude that it does not establish a sufficient basis to constitute a waiver of the right to a jury trial. Supreme Court Rule 615(a) (Ill. Rev. Stat. 1977, ch. 110A, par. 615(a)) permits us to notice defects affecting substantial rights even though they were not brought to the attention of the trial court. Trial by jury is such a fundamental constitutional right that the defendant's failure to raise the issue in his post-trial motion will not permit us to treat this matter as having been waived. (People v. Banks; People v. Miller (1977), 55 Ill. App.3d 1047, 371 N.E.2d 917.) We therefore conclude that the defendant has sustained his contention that he did not waive his right to trial by jury and his conviction must be reversed and the cause remanded for a new trial.

II.
In his appeal defendant raised additional issues concerning the sufficiency of the evidence of his guilt, and pursuant to People v. Taylor (1979), 76 Ill.2d 289, 391 N.E.2d 366, we have reviewed the evidence herein. He contends that the State's evidence did not prove him guilty beyond a reasonable doubt. He maintains that the complainant was not able to describe the clothing he was wearing at the time of the incident, could not recall the position of his arms, had not seen the defendant for 8 or 9 months, and that her testimony should be viewed with suspicion because of her former intimate relationship with the defendant.
 3-5 The testimony of a single witness, if positive and credible, is sufficient to support a conviction although contradicted by the accused. (People v. Sparkman (1979), 68 Ill. App.3d 865, 386 N.E.2d 346.) Such identification will be strengthened to the extent of any prior acquaintance with the defendant. (People v. Lumpkin (1975), 28 Ill. App.3d 710, 329 N.E.2d 262.) While the unimpeached testimony of an alibi may not be disregarded (People v. McGee (1961), 21 Ill.2d 440, 173 N.E.2d 434), the trier of fact is under no obligation to believe alibi testimony even if given by a greater number of witnesses. (People v. Jackson (1973), 54 Ill.2d 143, 295 N.E.2d 462.) The bias of a witness, whether it be favorable to or adverse to the defendant, is always pertinent on the question of the credibility of the witness. (People v. Gonzales (1978), 67 Ill. App.3d 215, 384 N.E.2d 788.) In the case at bar, the trial court specifically noted that the complainant had viewed the defendant under circumstances that would permit a positive identification, that she knew the defendant, and was positive she saw him with a brick in his hand. The court also took note that there were some discrepancies between the testimony of the *539 defendant and his defense witness as to whether he went out of her house on the evening of the incident. In addition, the defendant's argument that the complainant had reason to be biased against the defendant fails to take into consideration that Sandra Mendyk, the defense witness, may have been biased in his favor since she admitted an intimate relationship with the defendant. The weight and credibility to be afforded a witness' testimony is a determination for the trier of fact and, unless that determination is so unreasonable as to raise a reasonable doubt of defendant's guilt, it will not be disturbed on appeal. (People v. Harrison (1978), 57 Ill. App.3d 9, 372 N.E.2d 915.) We find no basis to conclude that a reasonable doubt of defendant's guilt existed based on the evidence presented.

III.
 6 Since this matter must again be tried, we shall consider defendant's contention that the restrictions placed upon his counsel's cross-examination of the complainant denied his right of due process and prevented him from establishing her bias, prejudice or predisposition against him. A witness may be cross-examined to establish that his testimony might be influenced by interest, bias or motive to testify falsely; however, in order to be admissible, such evidence must be positive and direct  not remote and uncertain. (People v. Curtis (1977), 48 Ill. App.3d 375, 362 N.E.2d 1319.) As a general rule, the latitude to be allowed in cross-examination of witnesses rests largely in the discretion of the trial court. Such cross-examination should be kept within fair and reasonable limits, and it is only in a case of clear abuse of such discretion, resulting in manifest prejudice to the defendant, that a reviewing court will interfere. (People v. Gallo (1973), 54 Ill.2d 343, 297 N.E.2d 569; People v. Brown (1974), 20 Ill. App.3d 1064, 313 N.E.2d 488.) Here, the defense counsel was permitted to question the complainant concerning her relationship with the defendant. However, the trial court sustained objections to those questions regarding the complainant's relationship with other men which appeared to have no connection to the relationship between her and the defendant. Similarly, the court did not allow defense counsel to question the complainant about the nature of the problem for which she had received psychiatric treatment. In each instance defense counsel abandoned the matter without making an offer of proof as to the relevancy of such questions. We do not find from the record presented that the trial court committed any abuse of discretion which resulted in prejudice to the defendant.
Since we have determined that the defendant must be given a new trial at which time all relevant evidence may be introduced, we need not *540 consider defendant's final contention that the trial court erred in denying his motion for a new trial based on newly discovered evidence.
For similar reasons we vacate the judgment of the trial court denying defendant's section 72 petition.
Judgment in cause No. 79-35 reversed and remanded.
Judgment in cause No. 79-36 vacated.
LINN, P.J., and JOHNSON, J., concur.
