Set Theory and Algebra MCQ - Sets

21:

Let R be a relation "(x -y) is divisible by m", where x, y, m are integers and m > 1, then R is

A.	symmetric but not transitive
B.	partial order
C.	equivalence relation
D.	anti symmetric and not transitive
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	Option: C Explanation : Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

22:

If f : A ---> B is a bijective function, then f -1 of f =

A.	f o f^-1
B.	f
C.	f ^-1
D.	I_A(Identity map of the set A)
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	Option: D Explanation : Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

23:

The set of all real numbers under the usual multiplication operation is not a group since

A.	multiplication is not a binary operation
B.	multiplication is not associative
C.	identity element does not exist
D.	zero has no inverse
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	Option: D Explanation : Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

24:

If (G, .) is a group such that (ab)- 1 = b-1 a-1, ∀ a, b ∈ G, then G is a/an

A.	commutative semi group
B.	abelian group
C.	non-abelian group
D.	None of these
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	Option: B Explanation : Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

25:

If * is defined on R* as a * b = (ab/2) then identity element in the group (R*, *) is

A.	1
B.	2
C.	1/2
D.	1/3
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	Option: B Explanation : Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

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