Question

State the hypothesis and the conclusion of each conditional.

Combine the conditionals in Exercises 5 and 6 into a single biconditional.

Short answer

The biconditional of both the statements is “if and only if ”.

Step-by-step solution

Step 1. Define the biconditional.

If a conditional and its converse are both true then they can be combined into a single statement by using connector “if and only if”. Such a statement containing the words “if and only if” is defined as a biconditional. For example, “p if and only if q”.

Step 2. Rewrite the statements.

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

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

Step 3. Write the biconditional.

The biconditional would be “if and only if ”.

Therefore, the biconditional of both the statements is “if and only if ”.