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Q.

LET ‘ R ’ be the real line . consider the following subsets of the plane R X R . S={(x,y):y=x+1 and o<x<2} T={(x-y):x-y  is an integer} which of the following is true

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a

Both S and T are equivalence relation on R

b

Neither S and T is an equivalence relation on R

c

'S ’ is an equivalence relation on R bul T is not

d

T is an equivalence relation on R but S is not

answer is A.

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Detailed Solution

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Given that R is set of all real numbers

Given S=x,y:y=x+1,0<x<2

This is not reflexive, because 1,1 is not an element in the set S

Given T=x,y: x-y is an integer

This is equivalence relation because x,xTx,yTy,xT and it is transitive also

Therefore, S is not equivalence and T is equivalence relation

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LET ‘ R ’ be the real line . consider the following subsets of the plane R X R . S={(x,y):y=x+1 and o<x<2} T={(x-y):x-y  is an integer} which of the following is true