Question

Prove:
1. F ⊃ (∼T • A)
2. (∼T ∨ G) ⊃ (H ⊃ T)
3. F • O / ∼H • ∼T

Answer 1

`$\sim H \bullet \sim T$` is true based on the given statements and the information derived from them.

We are given that
`$F \bullet O$`. From this, we can infer that F is true and O is also true.

Now, let's use the first statement:
`$F \supset(\sim T \bullet A)$`. This statement says that if F is true, then both
`$\sim T$` and A are true.

Since we know that F is true, we can conclude that
`$\sim T \bullet A$` is true. This means that both
`$\sim T$` and A are true.

Moving on to the second statement:
`$(\sim T \vee G) \supset(H \supset T)$`. This statement says that if either
`$\sim T$` or G is true, then
`$H \supset T$` is true.

Now, let's consider the third statement:
`$\sim H \bullet \sim T$`. This statement says that both
`$\sim H$` and
`$\sim T$` are true.

Based on the second statement, we know that if either
`$\sim T$` or G is true, then
`$H \supset T$` is true. Since we have
`$\sim T$` as true from the third statement, we can conclude that
`$H \supset T$` is true.

Finally, combining the information from the first and second statements, we have
`$\sim T \bullet A$` and
`$H \supset T$` as true. This means that both
`$\sim T$` and A are true, and
`$H \supset T$` is true.