1. The number of all one-one functions from set A = {1, 2, 3} to itself is
a) 2
b) 6
c) 3
d) 1
2. A relation R from A to B is an arbitrary subset of
a) A × B
b) B × A
c) A × A
d) B × B
3. A relation R in a set A is said to be an equivalence relation, if R is
a) symmetric only
b) reflexive only
c) transitive only
d) All of these
4. A1 coincides with the set of all integers in Z which are related to ...A..., A2 coincides with the set of all integers which are related to ...B... and A3 coincides with the set of all integers in Z which are related to ...C... . Here, A, B and C are respectively
a) one, zero, two
b) zero, one, two
c) two, one, zero
d) one, two, zero
5. If (a, b) ÎR, where R is a relation, then
a) (a, b) is not an ordered pair
b) a = b only
c) ab = 1 only
d) a is related to b under the relation R
6. The relation R defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then, R is
a) symmetric
b) transitive
c) an equivalence relation
d) reflexive
7. The relation R in the set {1, 2, 3, ..., 13, 14} defined as R = {(x, y) : 3x - y = 0} is
a) reflexive
b) transitive
c) symmetric
d) None of these
8. Let R be the relation in the set Z of all integers defined by R = {(x, y) : x - y is an integer}. Then R is
a) reflexive
b) symmetric
c) transitive
d) an equivalence relation
9. If R is the relation defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1}, then R is
a) reflexive
b) symmetric
c) transitive
d) None of these
10. The relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is
a) reflexive
b) symmetric
c) transitive
d) reflexive and symmetric
The function f : N → N given by $latex \displaystyle f\left( x \right)=\left\{ {\begin{array}{*{20}{c}} {x+1,\text{ if x is odd}} \\ {x-1,\text{ if x is even}} \end{array}} \right.$ is
(a) injective
(b) surjective
(c) bijective
(d) many-one
