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Can we replace bi-directional operator by ex-nor operator in mathematical logic, when bi-directional operator gives tautology? e.g if there is A <=> B, then can we write it as (~a)(~b) + ab?

plzz elaborate
in Mathematical Logic by (23 points) | 26 views

2 Answers

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Yes we can.mathematically, both are same things just symbols for representing them are different.

But I have not seen anyone using XNOR is propositional logic since XNOR is a part of digital logic we use bi-directional only in propositional logic and XNOR in digital logic.

$a <=> b$

$(a → b) \wedge (b→ a)$

$(a’ \vee b) \wedge (b’ \vee a)$

$(a’ \wedge b’) \vee (b \wedge a)$

$a \odot b$
by (4.1k points)
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that means we can use (a′∧b′)∨(b∧a) in place of a<=>b if we have to check validity, satisfiability, etc like this type of question https://gateoverflow.in/1933/gate2014-1-53

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yes both $a<=>b$ and  $a \odot b$ are same thing
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