Answer:
1) A 2) 3)A 4)B
Step-by-step 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.
