Question

What is the truth value for the following conditional statement?

p: true
q: true

∼p → q

F T → T
T T → F
F T → F
T F → T

Answer 1

`F -T\rightarrow T`.

Explanation:

We are given that

p: true

q: true

The condition statement
`\\eg p\rightarrow q`

If p is true then
`\\eg p` is false.

If p is false then
`\\eg p` is true.

If
`\ neg p` is false and q is true then the value of
`\\eg p \rightarrow q` is true.

If
`\\eg p` is true and q is true then
`\\eg p \rightarrow q` is true.

If
`\ neg p` is true and q is false then the value of
`\\eg p \rightarrow q` is false.

If
`\\eg p` is false and q is false then the value of
`\\eg p \rightarrow q` is true.

`F-T\rightarrow T`

`T-F\rightarrow F`

`F -F\rightarrow T`

`T-F \rightarrow F`.

Answer 2

FT→T

Explanation:

If p is true, then ~p is false.

Now note that

• If a and b are both true, then a→b is true.
• If a is true, b is false, then a→b is false.
• If a is false, b is true, then a→b is true.
• If a and b are both false, then a→b is true.

In your case, both~p is false and q is true, then ~p→q is true too (or FT→T)