Question

Which is logically equivalent to the converse of a conditinal statement?

Answer 1

A conditional statement is logically equivalent to its contrapositive. Converse: Suppose a conditional statement of the form "If p then q" is given. The converse is "If q then p." Symbolically, the converse of p q is q p.

That means that the answer is B: Inverse of the original
Hope this helped.

Answer 2

Answer: B) inverse of the original

P and Q are any two logical statements

Writing "If P, then Q" can be written as
`P \to Q` to show a flow in the logic (P goes to Q)

The converse swaps P and Q to get
`Q \to P`, so it translates to "If Q, then P"

The contrapositive is logically equivalent to the original conditional. We can form a truth table to verify this.

A truth table can also be used to show that the converse and inverse are equivalent expressions. So
`Q \to P` (converse) is the same as
`\textasciitilde P \to \textasciitilde \ Q` (inverse). The squiggly tilde signs mean "not". So
`\textasciitilde P` means "not P".