Question

If p ↔ q is true, which compound statement has the same truth value? p → q is false and q → p is true. p → q is false and q → p is false. p → q is true and q → p is false. p → q is true and q → p is true.

Answer 1

Answer: p → q is true and q → p is true.

Explanation:

A bi-conditional statement (p↔q) is the conjunction of two true conditional statements.

i.e. ((p→q)∧(q→p)=p iff q or p↔q)

It means that p↔q means "p implies q or (p → q)" and "q implies p or (q → p)" , both are true conditional statements.

Therefore, if p ↔ q is true, then p → q is true and q → p is true.

Answer 2

Answer: Last choice (D) is correct:
`p\implies q \,\,\mbox{and}\,\,q\implies p`

Explanation:

The answer follows directly from the definition of the logical biconditional connection p ↔ q, defined as "p → q and q → p"