Logical Equivalence of x <=> y and (x-->y) ^ ((~x)-->(~y))

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Homework Help Overview

The discussion revolves around proving the logical equivalence between the expression x <=> y and the expression (x-->y) ^ ((~x)-->(~y)). This involves concepts from propositional logic.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants suggest various methods for proving the equivalence, including rewriting expressions and using truth tables. There is also a question about the level of specificity required for the proof.

Discussion Status

The discussion is active, with participants offering different approaches and questioning the requirements for the proof. Some guidance has been provided regarding the use of truth tables and rewriting expressions, but no consensus has been reached on a specific method.

Contextual Notes

There is an indication that participants may have varying levels of familiarity with the concepts involved, as evidenced by the comments about the necessity of understanding truth tables and the nature of the proof required.

aorick21
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Prove x <=> y is logically equivalent to (x-->y) ^ ((~x)-->(~y)).
 
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aorick21 said:
Prove x <=> y is logically equivalent to (x-->y) ^ ((~x)-->(~y)).

Please show some sort of work or at least tell us where you are stuck. We help with your homework, not do your homework.
 
Actually, x \Leftrightarrow y is shorthand for a longer expression. Which one? Now rewrite one of the subexpressions and you're done.

If you want more specific help, please refer to l46kok's post.

Also, how specific do you need the proof to be? Can you use "intuitive" rules or do you really have to produce a proof tree?
 
Last edited:
I'd just use a truth table.

If you don't know what that is, then I don't think you belong in math.
 
TimNguyen said:
I'd just use a truth table.

If you don't know what that is, then I don't think you belong in math.

Rubbish. If you do know what one is then perhaps you belong in computer science or electrical engineering?
 
Aoik: what is the contrapositive of ~x=>~y

p.s.: Matt, you crack me up.
 

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