Question

I NEED HELP QUICKLY.

When p is false and q is true, then p or q is ___ true.
A. Always
B. Sometimes
C. Never

If p is true and ~ q is false, then p ~ q is ___ false.
A. Always
B. Sometimes
C. Never

If p is true and q is true, then ~ p ~ q is ___ true.
A. Always
B. Sometimes
C. Never

If p q is true and q is true, then p is ___ true.
A. Always
B. Sometimes
C. Never

Answer 1

1. A

2. what does ~ mean??

3. what does ~ mean??

4. A.

Answer 2

1) A 2) 3)A 4)B

Explanation:

Hi there!

To check those options we have to make it visible in a Truth Table. (Below). Also as it is an exercise of Logical Implications I've assumed some arrows are missing. The symbol ~ = ¬ Check it below.

1. When p is false and q is true, then p or q is always true (Truth Table 1)

Look it down the Truth Table, we are dealing with a Logical Implication. If p does is False and Q is true, the only result is the truth for these operands.

2. Examining the second (Truth Table 2)

If p is true and ~ q is false, then p ~ q

Well, assuming it is:

If p is true and ~ q is false, then p →~ q

Just like the Truth Table below, In a Logical Implication only when we start by truth operand and then we get a False conclusion we'll have a False as a Result.

3. Focusing on the Third one.

Assuming it is a ~p→~q Take a look at the Truth Table 3. Same principle as well.

Look firstly to the Truth Table 1.

In a Logical Implication if we start we come to a truth, then it's Truth.

Now pass it on to the Truth Table 3

As with False and False we conclude truth too then the answer is

A.

4) If p q is true and q is true, then p is ___ true.

Again assuming it is

If p →q is true and q is true, then p is ___ true.

Let's examine, scrutinizing it from the conclusion, i.e. from back to forth

Only two options on our Truth Table fits the case (in yellow)

In a Logical Implication, in this case, since q is true p may be true or false. So p is sometimes true.