Homework N1 (due on February 13th at 12:30 pm) CSC220 --- Spring 2020 1. Determine whether each of these conditional statements is true or false (2 points): If 1+1=2, then 2+2=5. If 1+1=3, then 2+2-4. 2. Determine whether each of these pairs of sets are equal (2points): a),() b)(1,3,3,5,5,5), (5,3,1} 3. Determine whether these statements are true or false (2points): a)(O) E {0,{@}} b){t{0}}} = {0.{}} 4. What is the cardinality of each of these sets (2points): a) {{a}} b) {a,{a}} 5. A detective has Interviewed four witnesses to a crime. From the stories of the witnesses the detective has concluded that if the butler is telling the truth then so is the cook; the cook and gardener cannot both be telling the truth; the gardener and the handyman are not both lying: and if the handyman is telling the truth then the cook is lying. For each of the four witnesses, can the detective determine whether that person is telling the truth or lying? (3points) 6. What is negation of each of these propositions? (2 points) a. There is pollution in New Jersey. b. The summer in Main is hot. 7. Let P and Q be the propositions, P: It is below freezing. Q: It is snowing. Express these as English propositions: (2 points) a. -PVO b. PA(PV) 8. Write these propositions using the above P and Q and logical connectives: (2 points) a. It is below freezing but not snowing. b. It is either below freezing or it is snowing. 9. Construct a truth table for each of these compound propositions: (3 points) a. (p= )=(V p) b. (piq) (9 ) c. -p (9 ) 10. Use a truth table to verify: (2 points) a. pV(19)p 11. Prove that if n is a positive integer, then n is odd if and only if 5n+6 is odd (2 points). 12. For each of the following sets, determine whether {2} is an element of that set (2 points). a. (2.2)) b. {{{2}}} 13. What is the Cartesian product of AXB, where A={0,1} and B={1,2} (2 points)