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Set Theory and Algebra MCQ - Sets

46:  

 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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47:  

A subset H of a group(G,*) is a group if 

A.

a,b ∈ H  a * b ∈ H

B.

a ∈ Ha-1 ∈ H

C.

a,b ∈ H  ⇒ a * b-1 ∈ H

D.

H contains the identity element

 
 

Option: C

Explanation :

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48:  

 If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is

A.

symmetric only

B.

anti-symmetric only

C.

both symmetric and anti-symmetric

D.

an equivalence relation

 
 

Option: C

Explanation :

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49:  

Which of the following statements is true?

A.

Every equivalence relation is a partial-ordering relation.

B.

Number of relations form A = {x, y, z} to B= {1, 2} is 64.

C.

Empty relation  φ is reflexive

D.

Properties of a relation being symmetric and being ant-symmetric are negative of each other.

 
 

Option: B

Explanation :

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50:  

 Let A = {1, 2, .....3 }
Define ~ by x ~ y  ⇔ x divides y. Then ~ is

A.

relexive, but not a partial-ordering

B.

symmetric

C.

an equivalence relation

D.

a partial-ordering relation

 
 

Option: D

Explanation :

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