If A and B then C?

Asked Nov 27 '16 at 18:29

Active Nov 27 '16 at 19:22

Viewed 6,130 times

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I'm working on a mathematical proof, but the problem I'm having is more to do with logic than math per se.

I'm wondering if these two are equivalent:

If A and B then C

If A and not B, then not C.

asked Nov 27 '16 at 18:29

lithium123

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If and only if "B then C", right? – Joseph Weissman Nov 27 '16 at 18:30
It's just a one way implication, if that clarifies something. – lithium123 Nov 27 '16 at 18:32
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NO, check it with truth table. – Mauro ALLEGRANZA Nov 27 '16 at 18:45

1 Answers1

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No, since they have different truth conditions: (A∧B)→C is false only when A=T,B=T,C=F, while (A∧~B)→~C is true in that case. You can verify this using truth tables.

answered Nov 27 '16 at 19:22

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