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If both the conditional statement and its converse are true, then they can be combined to form a biconditional statement.

a) True
b) False

1 Answer

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Final answer:

The statement is true; when both a conditional statement and its converse are true, they can be combined to create a biconditional statement which means that the antecedent and consequent are necessary and sufficient for each other.

Step-by-step explanation:

If both the conditional statement and its converse are true, they can indeed be combined to form a biconditional statement. A conditional statement is expressed in the form "if antecedent, then consequent". For example, "If it rains, then the ground gets wet". Its converse would be "If the ground gets wet, then it rains". If both these statements are true, we can combine them into a biconditional, which is stated as "The ground gets wet if and only if it rains". This biconditional indicates that the two conditions are both necessary and sufficient for each other.

Biconditional statements are crucial in logical reasoning and mathematical proofs because they establish the precise conditions under which statements are true. Hence, the statement in question is true.

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