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Set Theory and Algebra MCQ - Algebra

21:  

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 :

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22:  

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 :

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23:  

 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 relexive relations in A, then R - R' is reflexive

 
 

Option: D

Explanation :

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24:  

 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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25:  

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

A.

a,b ∈ H=> a * b ∈ H

B.

a ∈ H => a-1 ∈ H

C.

a,b ∈ H=> a * b-1 ∈ H

D.

H contains the identity element

 
 

Option: C

Explanation :

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