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this post was submitted on 23 Jul 2023
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So observing that this looks true because a OR b only fails when both a and b do, here's an alternative:
a OR b -> c
Conditional contraposition:
~c -> ~(a OR b)
De Morgan's law 1:
~c -> ~a AND ~b
I'm not actually sure what this kind of distribution is called, but it makes sense:
(~c -> ~a) AND (~c -> ~b)
Two more contrapositions:
(a -> c) AND (b -> c)