The contrapositive statement of the statement "if the show is a new episode, then I will record it” will be: "if the show is not a new episode, then I will not record it”.
What is a contrapositive statement?
The contrapositive statement is defined as, if there is a if statement is given, then the contrapositive statement will be estimated by interchanging the hypothesis and the conclusion of the inverse of the same conditional statement.
In another way, we can say that for finding the contrapositive statement, we have to first find the inverse of the given statement and then exchange the roles of the hypothesis and conclusion.
Mathematically, the contrapositive statement of the conditional statement p→q will be ~p→~q.
So here the statement is given by: "if the show is a new episode, then I will record it."
where p is the show is a new episode and q is I will record it.
then, ~p will be the show is not a new episode
~q will be I will not record it.
Then the contrapositive statement will be: "if the show is not a new episode, then I will not record it”.
Therefore, The contrapositive statement of "if the show is a new episode, then I will record it” will be "if the show is not a new episode, then I will not record it”.
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