Question
GIVE A DETAILED EXPLNATION FOR EACH PROBLEM
Find a proposition with three variables p, q, and r that is true when p and r are true and q is false, and false otherwise. Find a proposition with three variables p, q, and r that is true when at most one of the three variables is true, and false otherwise. Find a proposition with three variables p, q, and r that is never true. Determine whether p rightarrow (q r) and p rightarrow (q r) are equivalent. Determine whether p rightarrow (q rightarrow r) is equivalent to (p rightarrow q) rightarrow r. Determine whether (p rightarrow q) ( p rightarrow q) q. Show that (p V q) and q p are equivalent using a truth table. using logical equivalences. Show that each of the following propositions are tautology using logical equivalences: Write a proposition equivalent to p q using only p,q, and the connective v. Write a proposition equivalent to p rightarrow q using only p,q, and the connective What are the converse and contrapositive of the statement "If it is sunny, then I will go swimming"? Determine whether the compound propositions in [a]-[b] are satisfiable. Suppose that Q(x) is the statement "x + 1 = 2x." What are the truth values of In [a]-[c] P(m,n) means "m n", where the universe of discourse for m and n is the set of nonnegative integers. What is the truth value of the statement?
Explanation / Answer
7) p ?
