Answer :
Final answer:
The equivalent statement to "If the seals are tight, then the pipes are not leaking" is "If the pipes are leaking, then the seals are not tight." This is the contrapositive of the original statement, which maintains the same truth value. Therefore, this choice is logically equivalent to the original conditional statement.
Explanation:
Understanding Logical Equivalence
The statement provided is a conditional statement: If the seals are tight, then the pipes are not leaking. In symbolic logic, this can be represented as P → Q, where P is "the seals are tight" and Q is "the pipes are not leaking."
To find the equivalent statement, we need to examine the contrapositive, which states that if Q is false, then P must also be false. This can be expressed as: If the pipes are leaking (not Q), then the seals are not tight (not P). Therefore, the contrapositive of the original statement is If the pipes are leaking, then the seals are not tight.
To confirm: the correct choice from the provided options is: If the pipes are leaking, then the seals are not tight. This statement maintains the same truth value as the original statement, thus confirming its equivalence.
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