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6 . If R = {(1, 2),(2, 3),(3, 3)} be a relation defined on A= {1, 2, 3} then R . R (= R2) is
A. {(1, 2),(1, 3),(3, 3)}
B. {(1, 3),(2, 3),(3, 3)}
C. {(2, 1),(1, 3),(2, 3)}
D. R itself

7 . Which of the following statements is false ?
A. If R is relexive, then R ∩ R-1 ≠ φ
B. R ∩ R-1 ≠ φ   =>R  is anti-symmetric.
C. If R, R' are relexive relations in A, then R - R' is reflexive
D. If R, R' are equivalence relations in a set A, then  R ∩ R'  is also an equivalence relation in A

8 . If (G, .) is a group, such that (ab)2 = a2 b2 ∀ a, b ∈ G, then G is a/an
A. abelian group
B. non-abelian group
C. commutative semi group
D. none of these

9 . (Z,*) is a group with a*b = a+b+1 ∀ a, b ∈Z. The inverse of a is
A. 0 B. -2
C. a-2 D. -a-2

10 . Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an
A. subgroup
B. ininite, abelian
C. finite abelian group
D. infinite, non abelian group




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