Classical

Set Theory and Algebra MCQ - Sets

41:  

Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?

A.

g = g-1 for every g ∈ G

B.

g = g2 for every g ∈ G

C. (g o h) 2 = g2o h2 for every g,h ∈ G
D.

G is of finite order

 
 

Option: C

Explanation :


42:  

If the binary operation * is deined on a set of ordered pairs of real numbers as
(a, b) * (c, d) = (ad + bc, bd)
and is associative, then
(1, 2) * (3, 5) * (3, 4) equals

A.

(74,40)

B.

(32,40)

C.

(23,11)

D.

(7,11)

 
 

Option: A

Explanation :


43:  

 If A = (1, 2, 3, 4). Let  ~ = ((1, 2), (1, 3), (4, 2). Then  ~ is

A.

not anti-symmetric

B.

transitive

C.

reflexive

D.

symmetric

 
 

Option: B

Explanation :


44:  

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 equivalence relations in a set A, then R  ∩ R' is also an equivalence relation in A.

D.

If R, R' are reflexive relations in A, then R - R' is reflexive

 
 

Option: D

Explanation :


45:  

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

A.

R itself

B.

{(1, 2),(1, 3),(3, 3)}

C.

{(1, 3),(2, 3),(3, 3)}

D.

{(2, 1),(1, 3),(2, 3)}

 
 

Option: C

Explanation :




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