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.

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.

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

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

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

Final Answer