Question

If a → b is true, then ~a → b is also true.

Answer 1

Answer:

False

Step-by-step explanation:

To determine whether the statemaent "If $a\Rightarrow b$ is true, then $\neg a\Rightarrow b$ is also true" holds, you can form the truth table:

$\begin{array}{ccccc}a&b&a\Rightarrow b&\neg a&\neg a\Rightarrow b\\1&1&1&0&1\\1&0&0&0&1\\0&1&1&1&1\\0&0&1&1&0\end{array}$

When the result of the column $a\Rightarrow b$ takes value 1 (true), the result of the column  $\neg a\Rightarrow b$ is not always 1, then the statement is false.