# Set Theory and Algebra MCQ - Sets

56:

Let s(w) denote the set of al the letters in w where w is an English word. Let us denote set equality, subset and union relations by =, and respectively.

Which of the following is NOT true?

 A. s(ten) ⊂ s(twenty) B. s(stored) = s(sorted) C. s(sixty) ⊂ (s(six)  ∪ s(twenty) D. None of these Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
57:

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 Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:  ≤ -1)                { x2         (-1  ≤ x  ≤1)                {2 - x        (x  ≥ 1) Then value of f (-1.75) + f (0.5) + f (1.5) is '>
58:

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 Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:  ≤ 5. The realation R is '>
59:

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}} Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
60:

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 Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here:  ≠ 0 } III. Z = { x | x-8  = 4 } '>