forked from GitHub/gf-core
9 lines
435 B
Plaintext
9 lines
435 B
Plaintext
We will show that (A -> B) v (B -> A).
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To that end, we will assume ~ ((A -> B) v (B -> A)) and show _|_.
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So let us assume that ~ ((A -> B) v (B -> A)).
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Then, by the first de Morgan's law, we get ~ (A -> B) & ~ (B -> A) to prove _|_.
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So by splitting we get ~ (A -> B), ~ (B -> A) to prove _|_.
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By implication negation, we get A, ~ (B -> A) to prove _|_.
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By implication negation, we get A, ~ A to prove _|_.
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Hence we get _|_ as desired.
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