Chapter 0.1, Problem 4E

Determine whether each of the following implications is true or false.

If $7$ is even, then $25$ is odd.

If $7$ is odd, then $25$ is odd.

If $7$ is even, then $25$ is even.

If $7$ is odd, then $25$ is even.

If $\sqrt[3]{-8}=-2$, then $\sqrt{4}=\pm 2$.

If $\sqrt[3]{-8}\ne -2$, then $\sqrt{4}=\pm 2$.

If $\sqrt[3]{-8}=-2$, then $\sqrt{4}\ne \pm 2$.

If $\sqrt[3]{-8}\ne -2$, then $\sqrt{4}\ne \pm 2$.

If $\sqrt{x^2}=x$, then $\frac{1}{x+y}=\frac{1}{x}+\frac{1}{y}$.

If $\sqrt{x^2}=x$, then $\frac{1}{x+y}\ne \frac{1}{x}+\frac{1}{y}$.

If $\sqrt{x^2}\ne x$, then $\frac{1}{x+y}=\frac{1}{x}+\frac{1}{y}$.

If $\sqrt{x^2}\ne x$, then $\frac{1}{x+y}=\frac{1}{x}+\frac{1}{y}$.