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when p is false and q is true then p or q is

Mathematics
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I am guessing you are looking for the truth statement, yes? If p is true, then ~p is false (since ~p is the opposite of p). Remember that "^" means "and". The statement p ^ q is only true if BOTH p AND q are true (hence the "and"). Since ~p is false, we automatically know that ~p ^ q is false (q doesn't have to be factored in at all). Finally, remember that p <-> q is only true if the truth values for p and q are the same. So if p and q are both true, or both false, then p <-> q is true. Think of this as an "equals" (ie p = q). Because r is true, ~r is false. Since ~p ^ q is false as well, ~p ^ q and ~r have the same truth values. So (~p ^ q) <-> ~r is true. Here's one way you could write all this out: (~p ^ q) <-> ~r (~T ^ F) <-> ~T (F ^ F) <-> F F <-> F T
I just finished this portion in Geometry(:
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