I know that "if a then b" is represented as $a \implies b$, but how is "if a then b else c" represented?
I know in most programming languages there's a way to write this, but is there a way to write it in logic notation? Thanks in advance :]
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6$(a \implies b) \wedge ((\neg a) \implies c)$? – Chris Eagle Dec 19 '23 at 17:23
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@ChrisEagle Ah, thank you! This is exactly what I was looking for. – The_Animator Dec 19 '23 at 17:23
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Oh @ChrisEagle, by the way, is there a way you could write this as an answer instead of a comment? I hear questions answered in the comments get closed. – The_Animator Dec 19 '23 at 17:31
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The expression you want is $(a \implies b) \wedge ((\neg a) \implies c)$.
(This was previously a comment; posting it as an answer as requested)
Chris Eagle
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Quick follow-up — would we need the parenthesis around the ¬a if they were close enough that is just implied that the a was negated and not the (a => c)? – The_Animator Jan 03 '24 at 17:19
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1This is a matter of convention. I think the most common convention is that $\neg$ has priority over any of the binary connectives, so that $\neg a \implies c$ should be read as $(\neg a) \implies c$ anyway, but I also think that it is just clearer to put the parentheses in and leave nothing to chance. – Chris Eagle Jan 03 '24 at 20:12