Question

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

Answer 1

False

Explanation:

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

`\begin{array}{ccccc}a&b&a\Rightarrow b&\\eg a&\\eg 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
`\\eg a\Rightarrow b` is not always 1, then the statement is false.