# Set Theory and Algebra MCQ - Sets

121:

Consider the following statements :
S1 : There exist infinite sets A, B, C such that A  (B  C) is finite.
S2 : There exist two irrational numbers x and y such that (x + y) is rational.
Which of the following is TRUE about S1 and S2?

 A. Only S1, is correct B. Only S2 is correct C. Both S1 and S2 are correct D. None of S1 and S2 is correct Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here:
122:

Let R denote the set of real numbers.
Let f: R x R → R x R be a bijective function deined by f(x, y) = (x + y, x - y).

The inverse function off is given by

 A. B. f -1(x,y) = (x - y, x + y) C. D. f-1(x,y)=[2(x - y), 2(x + y)] Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
123:

Let f : A  B be a function, and let E and F be  subsets of A.

S1 : f(E  F) = f(E) ∪ f(F)

S2 : f(E ∩ F) = f(E)  f(F)
Which of the following is TRUE about Si and S2?

 A. Only S1 is correct B. Only S2 is correct C. Both S1 and S2 are correct D. None of S1 and S2 are correct Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here:
124:

The binary relation
r = {(1, 1), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2),(3,3), (3, 4)}
on the set A = {1, 2, 3, 4} is

 A. reflexive, symmetric and transitive B. neither reflexive, nor irreflexive but transitvie C. irreflexive, symmetric and transitive D. irreflexive and antisymmetric Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
125:

Let x and y are sets and I x I and l y I are their respective cardinalities. It is given that there are exactly 97 functions from x to y. From this one can conclude that

 A. │x│ = 1, │y│ = 97 B. │x│ = 97, │y│= 1 C. │x│ = 97, │y│= 97 D. none of these Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here: