Q:

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

Accepted Solution

A:
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 -> qtrue -> falseThe 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 trueWe 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 -> trueSo 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 -> falseThis 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/1466393brainly.com/question/1687476#LearnwithBrainly