please help i need right answers asap

MTH215. computing foundation!!!

QUESTION 15 Given U={r,s,t,u,v,w,x,y,z},A={u,w,x,y}.B={s,t,u,v,w}. find the following sets. Find the truth table of the following logical expression: (pq)(pq). (Note: Type T for true or F for false) QUESTION 5 What set does the below Venn diagram picture reprresent? a. A b. B c. AB d. AB e. Ac f. Bc g. (AB)c h. (AB)c i. AB j. BA Given two propositions: p="8mod2=1" and q= "The square root of 25 is 6" ". Answer the following questions with either T (if true) or F (if false) a. What is the truth value of the proposition p ? b. What is the truth value of the proposition q? c. What is the truth value of the statement "It is not the case that 8mod2=1 and the square root of 25 is 6 " QUESTION 7 Simplify the following logical expression: p[q(qp)] A. q b. T c. pq d. p e. pq Simplify the set expression A(A(ABC)) B I Parapraph Anal QUESTION 9 Simpldy the set expression A(B(BCA)) Given set A determine if the following statements are true or false. (Enter T for true and F for false.) A={a,b,{a,b},{c,d},e,{f}} a. a,bA b. {a,b}A c. {c,d}A d. {a,b}A e. [(f)}A QUESTION 11 Identify the law of logic used in the following simplification step: (pq)(pq)(pq) a. Idempotent law b. Annihilation law c. Absorption law d. Identity law e. Inverse law Identify the law of logic used in the following simplification step: r(pqrs)r a. Identity law b. Inverse law c. Idempotent law d. Absorption law e. Annihilation law QUESTION 13 If A={a,b,c,d,e} then S(A)= QUESTION 14 If P(B)=128 then B= For the following Venn diagram, determine the set BC. a. {2,4,a,h) b. {2,10,11,h,k} c. {6,7,12,14} d. {10,11,d,k} e. {5,7,14,15} f. {4,a,d) g. {6,12,d) h. {4,7,14,a} Given two sets A={1,2,3} and B={a,b,c}. Let AB be the cartesian product of A and B. Answer part (a) and (b) with T if true or F if false. a. (1,c)/AB. b. {(2,1),(3,a)}AB. Answer part (c) and (d) with a number. c. How many elements are there in the set AB ? d. What is P(AB) ? QUESTION 22 Given the predicate form below, find the enumerated form. S={xZ(2x4)(x+3)(x21)=0} a. {2,1,3} b. {2,1,1,3} c. (3,1,1,2) d. {3,1,2} Determine if the following logical expression is a tautology or contradiction. (pq)(qp) Tautology Both tautology and contradition Neither tautology nor contradiction Contradiction