Item 3.3.7.c.

The contrapositive in words is: for any number \(x\text{,}\) if there is some number which when multiplied by \(x\) does not give zero, then there is some number which when added to \(x\) does not give that number. In symbols: \(\forall x (\exists z (x\cdot z \ne 0) \imp \exists y (x + y \ne y))\text{.}\) We know the contrapositive must be true because the original implication is true.