Question

If p → q is true, then ~ p → ~ q is __________ true. Sometimes Always Never

Answer 1

Answer:

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

N

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. 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 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.