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September 30th, 2012, 11:56 AM   #1
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Logical equivalence!!

How to prove this logical equivalence without using truth table!!
[(pq)(qr)(rp)[(pq)(qr)(rp)]
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September 30th, 2012, 05:03 PM   #2
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Re: Logical equivalence!!

Hello, eChung00!

The proof is not difficult.
I hope I can explain my reasoning clearly.


Quote:
[latex]\text{Prove (without using truth tables):}













[color=beige]n . . [/color]

[color=beige]. . . [/color]






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September 30th, 2012, 05:15 PM   #3
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Re: Logical equivalence!!

Quote:
Originally Posted by soroban
Hello, eChung00!

The proof is not difficult.
I hope I can explain my reasoning clearly.


Quote:
[latex]\text{Prove (without using truth tables):}


p\,\leftrightarrow\,q)\,\wedge\,(q\,\leftright arrow\,r)\,\wedge\,(r\,\leftrightarrow\,p)" />


p \to q)\,\wedge\,(q\to r)\,\wedge\,(r\to p)" />

Oh.. nice!!!thanks..!!



p \to q)\,\wedge\,(q\to r)\,\wedge\,(r\to p)" />

p \to r)\;\text{ (Law of Syllogism)" />

[color=beige]n . . [/color]q\to p)" />

[color=beige]. . . [/color]r\to q)" />




p\,\leftrightarrow\,q) \,\wedge\,(q\,\leftrightarrow\,r)\,\wedge\,(r\,\le ftrightarrow\,p)" />

eChung00 is offline  
September 30th, 2012, 05:17 PM   #4
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Re: Logical equivalence!!

How can i edit the post!!lol
anyway Thank you very much!!!
eChung00 is offline  
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