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Question: 2 if the truth value of prqr is true and...

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2) If the Truth value of (p→r)--(q→r) is True and the truth value of p is True and r is False what is the Truth value of q a. b. Draw the truth table and support your answer 3) Determine whether the following statements are logically equivalent: a. p-(q->r) and (p-q->r 4) Show that (p-q)rs) and (p-r)- (qs are not logically equivalent. 5) Prove that the converse and inverse of a conditional statement are logically equivalent to each other a. Using Truth table b. Using logical equivalent In the following statements define the prepositions and write them in the symbolic form. (Assume that all variables represent fixed quantities or entities, as appropriate.) 6) a. If P is a square, then P is a rectangle b. If n is prime, then n is odd or n is 2. c. g. If n is divisible by 6, then n is divisible by 2and n is divisible by 3. 7) Find the negation, contraposition, inverse and covers of each statement in problem 6 8) Prove that p-(qVr) (pAris tautology as a result p (qVr) and (pAq-r are equivalent. 9) Determine the truth value of each of these statements if the domain of each variable consists of all real numbers a) 3x(x2-2) c) Vx(x2+221) 10) A stamp collector wants to include in her collection exactly one stamp from each country of Africa. If I(s) means that she has stamp s in her collection, F(s, c) means that stamp s was issued by country c, the domairn for s is all stamps, and the domain for c is all countries of Africa, express the statement that her collection satisfies her requirement. Do not use the 3 symbol 11) Let P(m, n) be “n is greater than or equal to m where the domain is the set of nonnegative integers. What are the truth values of n n P(m, n) and m 3n P(m, n)? 12) Translate these specifications into English where F (p) is “Printer p is out of service, B(p) is Printer p is busy, L(G) is Print job j is lost, and Q0) is Print job j is queued. a) 3p(F(p)AB(p))-3jLG) 13) Prove that all the solutions to the equation xx are irrational. 14) Prove that if n is integer and n2 +7 is even, then n is odd. a proof by contraposition. a proof by contradiction a. b. 15) Prove that if m and n are integers and mn is even, then m is even or n is even.

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