# Set Theory and Algebra MCQ - Sets

116:

If n  >  2, then number of surjections that can be defined from {1, 2, 3, ...n} onto (1, 2) is

 A. 2n B. nP2 C. 2n D. 2n-2 Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
117:

Consider the following relations :
R1 (a, b) iff (a + b) is even over the set of integers
R2 (a, b) iff (a + b) is odd over the set of integers.
R3 (a, b) ifa.b > 0 over the set of non zero rational numbers.
R4 (a, b) if I a - b I  < = 2 over the set of natural numbers.
Which of the following statements is correct ?

 A. R1 and R2 are equivalence relations, R3 and R4 are not B. R1 and R3 are equivalence relations, R2 and R4 are not C. R1 and R4 are equivalence relations, R2 and R3 are not D. R1, R2, R3 and R4 are all equivalence relations Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
118:

A relation on the integers 0 through 4 is defined by :
R = {(x, y) : x + y  2x).

Which of the properties listed below applies to this relation?
I.  Tronsitivity
II. Symmetry
III. Relexivity

 A. I only B. III only C. I and III D. II and III Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
119:

Let R1 and R2 be two equivalence relations on a set. Consider following assertions :
I.  R1  R2 is an equivalence relation.
II. R1  R2 is an equivalence relation.
Which of the following is correct ?

 A. Both assertions are true B. Assertion I is true but assertion II is not true C. Assertion II is true but assertion I is not true D. Neither I nor II is true Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
120:

A relation over the set S = {x, y, z} is defined by :
{(x, x), (x, y), (y, x), (x, z), (y, z), (y, y), (z, z)}.
What properties hold for this relation?

 A. Symmetric B. Reflexive C. Antisymmetric D. Irrelexive Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here: