Which form is a valid conditional statement?

• A. The conclusion follows if and only if the hypothesis is true.
• B. The hypothesis is true implies the conclusion only if the conclusion is true.
• C. If the conclusion is true, then the hypothesis is true.
• D. If the hypothesis is true, then the conclusion follows.

Answer: (D)

A conditional statement states that if the hypothesis is true, the conclusion must be true. The clean, standard form expresses this as: If the hypothesis is true, then the conclusion follows. That one-way implication is the essence of a conditional: P implies Q.

The other phrasings change the meaning. “If and only if” makes the statement bidirectional, asserting both P ⇒ Q and Q ⇒ P, which is stronger than a simple conditional. Reversing the order gives the converse, Q ⇒ P, which is not guaranteed by P ⇒ Q. The awkward “only if” formulation doesn’t present the straightforward conditional structure and can be confusing or fail to convey the intended implication.

So the form that states the hypothesis guarantees the conclusion in a one-way implication is the correct conditional.