Question

State the hypothesis and the conclusion of each conditional.

only if

Short answer

The hypothesis is and conclusion is .

Step-by-step solution

Step 1. Hypothesis and the conclusion.

The hypothesis and the conclusion of a conditional statement are where the hypothesis is the phrase immediately following by the word if and the conclusion is the phrase immediately following by the word then.

Step 2. Symbolic representation.

If p represents the hypothesis and q represents the conclusion, then the basic form of an if-then statement is “If p, then q”. For example, in the statement “If today is Friday, then tomorrow is Saturday”, “today is Friday” is the Hypothesis, and “tomorrow is Saturday” is the Conclusion.

Step 3. Rewrite the statement.

The given statement “ only if ” can be rewritten as “If , then ”.

Step 4. Identification of Hypothesis and the conclusion.

Since, “” is followed by “If” and “” is followed by “then” thus, the hypothesis is and the conclusion is .

Hence, the hypothesis is and the conclusion is .