geometry

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Given p is false, q is true,and r is false, find the truth value of the statement. (~P <____> ~Q) ____> ~r
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  • geometry -

    The <-> operator is true only if both operands have the same truth value, i.e. TT or FF.
    Given p is false and q is true, then ~p is true and ~q is false, therefore ~p <-> ~q is false.

    Since the conditional p->q is false only if p is true and q is false, here we have
    F->~r or
    F->T
    so it is true. Thus with p=F, q=T and r=F, the whole statement together is true,

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