I need explanation and correction to these questions

Q-2: The negation of (PQ)R is a) (PQ)R b) R(PQ) c) R(PQ) d) PQR e) None of the above 15: Suppose that R is an equivalence relation on A={1,2,3,4,5}. Which of the following could be a partition of A arising from R ? a) {1,2},{3,4}{1,2,3,4,5} c) {1,2,3,4} d) {1},{2,3},{3,4,5} e) None of the above AiAj= Ai=A 16: The maximal element of the poset (P(A),),A={1,2,3}, is a) 3 b) {3} c) {{3}} d) {1,2,3} e) None of the above Q-1: If S is a set such that S=3, then P(S)= a) 9 b) 8 c) 6 d) 3 e) None of the above Q-2: The contrapositive of (PQ)R is a) RPQ b) (PQ)R c) RPQ d) PQR e) None of the above Q-3: If a7mod13, then a may equal a) 0 b) 14 c) 19 d) 19 e) None of the above Q-4: If A={1,2,3} and B={4,5,6}, then AB= a) b) {1,2,3} c) {4,5,6} d) {1,2,3,4,5,6} e) None of the above Q-5: The hexadecimal representation of (1101101)2 is a) 6D b) D5 c) 155 d) 551 Q-1: [8+8 marks] a) Determine whether each of the following is TRUE or FALSE: i. 1+2=5 if and only if 31=1. F ii. 319 or 1423(mod4). iii. x+5>9 for every real number x. F iv. x(2x=x), domain is the set of integers. b) Show that the statement ((PQ)PQ) is a contradiction using: i. Truth table. solved ii. Logic laws. Q-2: [4+6+6 marks] a) Find the bit-wise XOR of strings 11010011 and 10111010 . 01101001 b) Let B(x),E(x) and G(x) be the statements " x is a book" " x is expensive" and " x is good" respectively. Express each of the following statements using quantifiers and logical connectives, where the universe of discourse is the set of all objects: i. All expensive books are good. " will used A instead the quantifiers "All", and E instead of "Some" ii. Some good books are not expensive. EE(x)E(x)=(x) c) Show that (BA)(CA)=(BC)A. Need to be solved Q-3: [6+4+6 marks] a) Find a,b and c if a=43div6a+b=51mod6.a+c=64mod8c=4b=1 b) Let a=23325 and b=223372. Find GCD(a,b) and LCM(a,b). acD=32 LCM=7560 c) Are the numbers 96 and 175 relatively primes? Explain. NO, both of then accept division. 96/3 and 175/5 product of A and B. b) Using the encrypting function f(p)=(p+10)mod26,0p25, encrypt the message "DEAR DOCTOR". product of A and B. b) Using the encrypting function f(p)=(p+10)mod26,0p25, encrypt the message "DEAR DOCTOR