Questions: Write out the contrapositive of this statement "if Jasmine goes to the meeting, then she will be elected vice-president". Also tell whether the original statement is necessarily equivalent to the contrapositive.

Write out the contrapositive of this statement "if Jasmine goes to the meeting, then she will be elected vice-president". Also tell whether the original statement is necessarily equivalent to the contrapositive.

Transcript text: Write out the contrapositive of this statement "if Jasmine goes to the meeting, then she will be elected vice-president". Also tell whether the original statement is necessarily equivalent to the contrapositive.

Solution

Solution Steps

To find the contrapositive of a conditional statement, we need to negate both the hypothesis and the conclusion and then reverse them. The original statement is "if Jasmine goes to the meeting, then she will be elected vice-president". The contrapositive of this statement would be "if Jasmine is not elected vice-president, then she did not go to the meeting". The original statement and its contrapositive are logically equivalent.

Step 1: Identify the Original Statement

The original statement is given as: \[ \text{if Jasmine goes to the meeting, then she will be elected vice-president} \]

Step 2: Formulate the Contrapositive

To find the contrapositive, we negate both the hypothesis and the conclusion and then reverse them. The contrapositive of the original statement is: \[ \text{if Jasmine is not elected vice-president, then she did not go to the meeting} \]

Step 3: Determine Logical Equivalence

In logic, a statement and its contrapositive are always logically equivalent. Therefore, the original statement and its contrapositive are necessarily equivalent.

Final Answer

The contrapositive of the statement "if Jasmine goes to the meeting, then she will be elected vice-president" is: \[ \boxed{\text{if Jasmine is not elected vice-president, then she did not go to the meeting}} \]

The original statement and its contrapositive are logically equivalent: \[ \boxed{\text{True}} \]

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