Set Theory and Algebra MCQ - Algebra

31:  

The universal relation A x A on A is

A.

an equivalence relation

B.

anti-symmetric

C.

a partial ordering relation

D.

not symmetric and not anti-symmetric

 
 

Option: A

Explanation :

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32:  

Total number of diferent partitions of a set having four elements is

A.

16

B.

8

C.

15

D.

4

 
 

Option: C

Explanation :

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33:  

A partition of {1, 2, 3, 4, 5} is the family

A.

((1, 2),(3, 4),(3, 5))

B.

(φ(1, 2),(3, 4),(5))

C.

{(1, 2, 3),(5)}

D.

{(1, 2,), (3, 4, 5)}

 
 

Option: D

Explanation :

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34:  

110.The matrices [cos 0    -sin0]   and  [a   0]
                                 [sin 0     cos0]            [0   b]
commute under the multiplication

 

A. if a = b (or) 0 = nit, n is an integer
B. always
C. never
D. if a cos 0 b sin 0
 
 

Option: A

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