If n > 2, then number of surjections that can be defined from {1, 2, 3, ...n} onto (1, 2) is
A. | 2n |
B. | ^{n}P_{2} |
C. | 2^{n} |
D. | 2^{n}-2 |
Option: D Explanation : Click on Discuss to view users comments. |
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 |
Option: B Explanation : Click on Discuss to view users comments. |
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 |
Option: C Explanation : Click on Discuss to view users comments. |
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 |
Option: C Explanation : Click on Discuss to view users comments. |