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Q.

If R1={(1,1)(2,2)(1,2)(2,1)(3,3)}  and R2={(1,1)(2,2)(2,3)(3,2)(3,3)}  are two relations in the set S={1,2,3} ,the incorrect statement is:

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a

R1R2  is an equivalence relations in S.

b

R1R2  is an equivalence relations in S.

c

None of These

d

R1 and R2  both are equivalence relations in S.

answer is C.

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Detailed Solution

R1R2 ={(1,1)(2,2)(1,2)(2,1)(3,2)(2,3)(3,3)} is an equivalence relations in S.

which is incorrect since 3,2,2,1R1R2 but 3,1R1R2  hence  not transtive.

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