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Peter
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- Math
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Hat (๐ โง ๐)โกT, must be that ๐โกT and ๐โกT, hence [(๐ โง ๐) โ ๐]โก ๐, and [[(๐ โง ๐) โ ๐] โ ๐ ]โก ๐ โ Fโกยฌ๐. Secondly, [(๐ โ ๐) โ ๐ ] from t
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Therefore proving that [[(๐ โง ๐) โ ๐] โ ๐ ] โ [(๐ โ ๐) โ ๐ ] โก T. Q.E.DTherefore proving that [[(๐ โง ๐) โ ๐] โ ๐ ] โ [(๐ โ ๐) โ ๐ ] โก T. Q.E.DTherefore proving that [[(๐ โง ๐) โ ๐] โ ๐ ] โ [(๐ โ ๐) โ ๐ ] โก T. Q.E.D
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herefore ๐ โจ (๐ โจ ๐)โกF. So for the left side, since no matter if it is ๐โกF or
(๐ โจ ๐)โกF, one out of the two possibility being false is certain, so necessarily ๐ โง (๐ โจ ๐)โกF, and since F FโกT, [๐ โง (๐ โจ ๐)] [(๐ โง ๐) โจ (๐ โง ๐)] is true.
And consider the second case where (๐ โง ๐) โจ (๐ โง ๐)โกT, for it to be held true, necessarily (๐ โง ๐)โกT or (๐ โง ๐)โกT. Hence either ๐ โง (๐ โง ๐) โกT or ๐ โง (๐ โง ๐) โกF. Thus for ๐ โง (๐ โจ ๐), its truth value must be T.
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