Question

For the statement below, find the contrapositive. If Mike does his Geometry homework, then he will get a good grade.

Answer 1

Remeber that given a proposition of the following form:

`p\Rightarrow q`

then, the contrapositive of the implication is:

`\\eg q\Rightarrow\\eg p`

in this case, we have the following:

`p\Rightarrow q\equiv\text{ If Mike does his Geometry homework, then he will get a good grade}`

then, the contrapositive is:

`\begin{gathered} \\eg q\Rightarrow\\eg p\equiv \\ \text{If Mike does not get a good grade, then he did not do his Geometry homework} \end{gathered}`