The statement (if p then q) is always true if p ends up being false, regardless of what q is. Why?
Notice that the statementes begins IF p...
So, everything that follows in the statement depends on p being true. If q is false and p true, then the statement is quite obviously false, because when p is true, q has to be true.
But, what happens when p is false? Then q does not matter. So the statement (if p then q) itself is still logically true, as the if condition was never actually triggered (because p is false).
Why is the statement true though? Because it is NOT false. When p is false, then the truth of q is irrelevant and can do nothing to contradict the conditional. Thus, the statement is NOT false. Thus, it must be true.
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How it works
Date: 2003-08-28 12:24 pm (UTC)Notice that the statementes begins IF p...
So, everything that follows in the statement depends on p being true. If q is false and p true, then the statement is quite obviously false, because when p is true, q has to be true.
But, what happens when p is false? Then q does not matter. So the statement (if p then q) itself is still logically true, as the if condition was never actually triggered (because p is false).
Why is the statement true though? Because it is NOT false. When p is false, then the truth of q is irrelevant and can do nothing to contradict the conditional. Thus, the statement is NOT false. Thus, it must be true.
I hope that was clear.