Logical Implications: A, C, and the Outcome

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Anyone know what the answer to this would be?
A implies B
C implies not B
What happens when both A and C occur?

I just asked my brother if he wanted to play basketball with me and my father. He said (as a joke) if I were going, he wouldn't go, but if my father were going, he would go. We were both going. So mathematically, which would he do?
 
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The statemetn (A \Rightarrow B) \wedge (C \Rightarrow \neg B) \wedge (A \wedge C) is identically false. IOW your brother lied. :smile:
 
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