If a Huskies game will not be on television, then Victoria will buy tickets for it.
If a Huskies game will be on television, then Victoria will not buy tickets for it.
Is the second conditional the contrapositive, converse, or inverse of the first conditional?
The second conditional is the converse of the first conditional.
The second conditional is the inverse of the first conditional. According to the definition of inverse, when the antecedent and consequent of a conditional statement are negated, the resulting statement is the inverse.
To determine the relationship between the second conditional statement and the first conditional statement, let's define the terms:
First conditional statement:
If a Huskies game will not be on television, then Victoria will buy tickets for it.
Second conditional statement:
If a Huskies game will be on television, then Victoria will not buy tickets for it.
Contrapositive:
The contrapositive of the first conditional statement flips the hypothesis and the conclusion, and negates both. The contrapositive of the first conditional statement would be:
If Victoria does not buy tickets for a Huskies game, then it will be on television.
Converse:
The converse of the first conditional statement switches the positions of the hypothesis and conclusion without negating them. The converse of the first conditional statement would be:
If Victoria buys tickets for a Huskies game, then it will not be on television.
Inverse:
The inverse of the first conditional statement negates both the hypothesis and the conclusion. The inverse of the first conditional statement would be:
If a Huskies game will be on television, then Victoria will buy tickets for it.
Comparing the second conditional statement with the options provided, we can conclude that the second conditional statement is the converse of the first conditional statement.