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(∀x∀yP(x,y))→(∀x∀yP(y,x)) is tautology or not??

in Mathematical Logic
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(∀x∀yP(x,y))→(∀x∀yP(y,x)) is tautology or not??
in Mathematical Logic
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410 views

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by
Can you give an example?
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by

No its not tautology!!!

See this IV option https://gateoverflow.in/8259/gate2015-2_55

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it's not a tautology if the domains for X and Y are not same.
for example
P(X,Y) Girl X ties rakhi to Boy Y
now P(X,Y) is not same as P(Y,X)
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