Question

State the hypothesis and the conclusion of each conditional.

only if

Short answer

The hypothesis is and the 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 forms of an if-then statement are:

“If p, then q”

“p implies q”

“p only if q”

“q is p”.

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. Identification of the Hypothesis and the conclusion.

Since, the statement “ only if ” is similar to the statement “p implies q” where p represents the hypothesis and q represents the conclusion, therefore, the hypothesis is and the conclusion is .

Hence, the hypothesis is and the conclusion is .