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Is there a logic symbol for what output a logic gate yields?

For instance, for an AND gate:

A B A ^ B
T T T
T F F
F T F
F F F

I want to propagate A ^ B into output C, but I wouldn't want to use A ^ B → C because implication has a different truth table. Is A ^ B = C really the best option?

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Yes, if you mean that C is the same as A ∧ B, you can say C = A ∧ B. C ⇔ A ∧ B is also an option.

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It is not really clear what you are trying to do. Simply writing A ^ B already expresses what the conjunction of A with B yields.

A ^ B = C is not a well-formed formula in predicate logic. = is conventionally used as the identity predicate and cannot stand between propositions.

You are perhaps trying to express what goes on in a programming language when a value is assigned to a variable. In which case, different languages use different symbols, such as

   =    :=    <-    <<   
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