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21. Let R be a relation "(x-y) is divisible by m", where x, y, m are integers and m > 1, then R is
symmetric but not transitive
partial order
equivalence relation
anti symmetric and not transitive
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22. If f : A ---> B is a bijective function, then f -1of =
f o f -1
f
f -1
IA(Identity map of the set A)
23. The set of all real numbers under the usual multiplication operation is not a group since
multiplication is not a binary operation
multiplication is not associative
identity element does not exist
zero has no inverse
24. If (G, .) is a group such that (ab)- 1 = b-1 a-1, ∀ a, b ∈ G, then G is a/an
commutative semi group
abelian group
non-abelian group
None of these
25. If * is defined on R* as a * b = (ab/2) then identity element in the group (R*, *) is
1
2
1/2
1/3
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