b) Natalie, Oliver, Pinky, Queenie, and Robert are classmates. Out of the five young people, two of them are really honest, and they always tell the truth. The other three young people sometimes are honest and sometimes are not. When they were asked about who was a liar, the answers were as follows:
• Natalie said: "Oliver and Robert are not liars."
• Oliver said: "Pinky is a liar."
• Pinky said: "Queenie is a liar."
• Queenie said: "Robert is a liar."
• Robert said: "Oliver and Pinky are liars."
Determine which two young people are honest. (Steps required.)
c) Some properties of rational numbers are given:
• The sum of two rational numbers is a rational number.
• The difference of two rational numbers is a rational number.
• The product of two rational numbers is a rational number.
• The quotient of dividing two rational numbers is a rational number if the divisor is not zero.
Prove, or disprove, the following statements:
If p and q are rational numbers, q ≠0, and r is an irrational number, then p + rq is irrational.
d) Mrs. Ip was hurt by two people in a unicorn dance. Detective Tsang has identified four people: Chan, Lee, Cheung, and Wong, and has the following observations:
• If Wong hurt Mrs. Ip, then Lee is innocent.
• Cheung is innocent if Lee is innocent.
• If Wong did not hurt Mrs. Ip, then Chan hurting Mrs. Ip implies that Cheung also hurt Mrs. Ip.
• Lee hurt Mrs. Ip only if Chan hurt Mrs. Ip.
Determine which two people hurt Mrs. Ip.