Classical

Set Theory and Algebra MCQ - Sets

41:  

Let (Z, *) be an algebraic structure, where Z is the set of integers and the operation * is defined by n * m = maximum (n, m). Which of the following statements is TRUE for (Z, *) ?

A.

(Z, *) is a monoid

B.

(Z, *) is an abelian group

C.

(Z, *) is a group

D.

None of these

 
 

Option: D

Explanation :

Click on Discuss to view users comments.

Write your comments here:



42:  

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 :

Click on Discuss to view users comments.

Write your comments here:



43:  

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 :

Click on Discuss to view users comments.

Write your comments here:



44:  

 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 :

Click on Discuss to view users comments.

Write your comments here:



45:  

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 :

Click on Discuss to view users comments.

Write your comments here:






*********
X