Question

If p is true and q is false, the p -> q is always, sometimes, never true.

Answer 1

1. If p is true and q is false, the p -> q is never true.

2. When p is false and q is true, then p or q is always true.

3. If p is true and ~ q is false, then p -> ~ q is never false.

4. If p is true and q is true, then ~ p -> ~ q is always true.

5. If p -> q is true and q is true, then p is always true.

Further Explanation:

The logic gates are used here.

Here, the symbol -> is for implication. Implication p-> q means that if p is true then q must be true.

So let us look at all the questions one by one.

1. If p is true and q is false, the p -> q is always, sometimes, never true.

p -> q

true -> false

The true should imply true so the given statement will never be true.

2. When p is false and q is true, then p or q is always, sometimes, never true.

false or true

We know that in or gate even if one input is true, the whole output is true. So this statement will be always true given p is false and q is true.

3. If p is true and ~ q is false, then p -> ~ q is always, sometimes, never false.

This translates to:

true -> true

So it will never be false.

4. If p is true and q is true, then ~ p -> ~ q is always, sometimes, never true.

This translates to:

false -> false

This will always be true.

5. If p -> q is true and q is true, then p is always, sometimes, never true.

If p->q is true and q is true then p will always be true. "Implies to" states that in p->q, in order for q to be true p has to be true. So p will always be true.

Learn more at:

• brainly.com/question/1466393
• brainly.com/question/1687476

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