SOLUTION: If p q is true and q is true, then p is neveralwayssometimes tr

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Question 843102: If p q is true and q is true, then p is neveralwayssometimes tr
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
What is in between the p and the q?
Please repost.

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the symbol you were trying to show didn't show up.

the following truth table should give you your answer, since it covers all the most common symbols that you may have meant.



p         q         p v q      p ^ q     p ---> q      p <---> q

T         T           T          T          T              T
T         F           T          F          F              F
F         T           T          F          T              F
F         F           F          F          T              T



the first 2 columns are p and q individual states (either true or false)
the third column is p or q, with the v symbolizing or.
the fourth column is p and q, with the ^ symbolizing and.
the fifth column is p implies q, with the ---> symbolizing implies.
the sixth column is q if and only if p, with the <---> symbolizing if and only if.

the question was:
If p q is true and q is true, then p is never/always/sometimes true

If or is indicated (v), then the answer is sometimes, because the or condition only requires that one of them be true.

If and is indicated (^), then the answer is always, because the and condition requires both of them to be true.

if implies is indicated (--->), then the answer is sometimes because the implies condition allows q to be true regardless of whether p is true or false.

if if and only if is indicated (<--->), then the answer is always because the if and only condition requires both to be true.

In the truth table, if you only look at the lines where Q is true, you may be able to spot this better.

Only those lines are duplicated below:



p         q         p v q      p ^ q     p ---> q      p <---> q

T         T           T          T          T              T
F         T           T          F          T              F



you can see on the first line, that p is true and this allows all other conditions to be true.

on the second line p is false.
the or condition is still true and the implies condition is still true.
the and condition and the if and only if condition, require p to also be true so they are false.


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