fbpx

What is the contrapositive to this statement? Statement: If you feel hungry, then you eat.

    C. If you don’t eat, then you don’t feel hungry.

    The contrapositive to a statement is the inverse of the converse (or the converse of the inverse) of the statement. If ##p## and ##q## are conditions, then

    ##p=##You feel hungry. ##q=##You eat.

    Adding the symbol ##~## contradicts the condition.

    Therefore,

    ##~p=##You don’t feel hungry. ##~q=##You don’t eat.

    So, using these symbols, the original conditional statement would be expressed as

    ##p=>q##

    Meaning that the inverse of the statement would be expressed as

    ##~p=>~q##

    Because the inverse of a statement is contradicting both conditions.

    To find the contrapositive of the original statement, we need to find the converse of the inverse, so

    ##~q=>~p##

    Because the converse of a statement is making the hypothesis of the original statement (##p##) the new conclusion and the original conclusion (##q##) the new hypothesis. In other words, the two conditions switch order.

    Now that we have clarified that ##~q=>~p## Is the contrapositive of the statement, we can put it into words.

    (##~q##) If you don’t eat, (##~p##) then you don’t feel hungry.