Classical

Set Theory and Algebra MCQ - Sets

56:  

Let f : R → R be defined by

   f(x)=     {x+2       (x  ≤ -1)

               { x2         (-1  ≤ x  ≤1)

               {2 - x        (x  ≥ 1)

Then value of f (-1.75) + f (0.5) + f (1.5) is

A.

0

B.

2

C.

1

D.

-1

 
 

Option: C

Explanation :

≤-1)

{ x2 (-1x1)

{2 - x (x1)

Then value of f (-1.75) + f (0.5) + f (1.5) is

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57:  

A relation R is defined on the set of positive integers as xRy
 if 2x + y  ≤ 5.

The realation R is

A.

reflexive

B.

symmetric

C.

transitive

D.

None of these

 
 

Option: C

Explanation :

≤5.

The realation R is

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58:  

Let R be na equivalence relation on the set {1,2,3,4,5,6} given by

{(1,1),(1,5),(2,2),(2,3),(2,6),(3,2),(3,3),(3,6),(4,4),(5,1),(5,5),(6,2),(6,6),(6,6)}.

The partition included by R is

A.

{1,2,3,4,5,6}

B.

{{1,3,5,6},{2,4}}

C.

{{1,5},{2,3,6},{4}}

D.

{{1,2,3,4},{5,6}}

 
 

Option: C

Explanation :


59:  

Which of the following sets is a null set ?

I.  X = {x | x= 9, 2x = 4 } 

II. Y = {x | x= 2x.x  ≠ 0 }


III. Z = { x | x-8  = 4 }

A.

I and II only

B.

I, II and III

C.

I and III only

D.

II and III only

 
 

Option: A

Explanation :

≠0 }


III. Z = { x | x-8 = 4 }

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60:  

 A Relation R is defined on the set of integers as xRy if (x + y) is even. Which of the following statements is TRUE?

A.

R is not an equivalence relation

B.

R is an equivalence relation having one equivalence class

C.

R is an equivalence relation having two equivalence classes

D.

R is an equivalence relation having three equivalence classes

 
 

Option: C

Explanation :




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