How do you construct a truth table for q arrow p?

Answer 1

I guess you mean q → p (as in the logic operator: q implies p).

To create this truth table, you run over all truth values for q and p (that is whether each statement is True or False) and calculate the value of the operator. You can use True/False, T/F, 1/0, √/X, etc as long as you are consistent for the symbol used for True and the symbol used for False (the first 3 suggestions given are the usual ones used).

For implies:

• if you have a true statement, then it can only imply a true statement to be true
• but a negative statement can imply either a true statement or a false one to be true

giving:

. q . . p . q→p

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. 0 . . 0 . . 1 .

. 0 . . 1 . . 1 .

. 1 . . 0 . . 0 .

. 1 . . 1 . . 1 .