Multiple Choice Questions

1) The relation is defined on the setA= {1,2,3,4,5} by R={(a,b):|a^2-b^2|<16} is given by

a) {(1,1),(2,1),(3,1),(4,1),(2,3)}

b) {(2,2),(3,2),(4,2),(2,4)}

c){(3,3),(4,3),(5,4),(3,4)}

d) none of these

Ans d )none of these

2) The smallest equivalence relation on the set A= {1,2,3}is

a) {(1,1),(2,2),(3,3)}

b){(1,1)}

c){(1,1),(2,1),(3,1),(2,2),(2,3),(3,2)}

d) none of these

Ans a) {(1,1),(2,2),(3,3)}

3) If A = {1,2,3}and B ={1,4,6,9} and R is a relation from Ato B defined X is greater than y the range of R is

 a) {1,4,6,9}

b){4,6,9}

c) {1}

d) none of these

Ansc) {1}

4) A relation R is define from { 2,3,4,5 } {3,6,7 ,10} by x R y = x is relatively prime to y then domain of R is

 a) {2,3,5}

b.){3,5}

c ) {2,3,4}

d) {2,3,4,5}

Ans a) {2,3,5}

5) R is a realation from {11,12,13} to {8,10,12} defined by y=x-3 Then inverse of R is

a) {(8,11),(10,13)}

b.) {(11,8),(13,10)}

c) {(10,13),(8,11),(8,10)}

d) none of these

Ansa) {(8,11),(10,13)}
6) Let R be a relation on the set N of natural numbers defined by n R m iff n divides m Then R is

 a) Reflexive and symmetric 

b) Transitive and symmetric

 c) Equivalence

 d) Reflexive,transitive,but not symmetric

Ans d)

7) Maximum number of equivalence relations on the set A={1,2,3} is

a) 1

b). 2

c) 3

d) 5

Ans d ) 5

8) If the set A contains 7 elements and set B contains 10 elements then number of one one functions from A to B is
Ans b)

9) If A = {1,2,3,.....n} and B = {a,b}.Then number of subjections from A to B is

Ans (b)

10) If f(x)= px/x+1,xis not equal to -1 then for what values of p f(f(x))= x

a) √2

b) -√2

c) 1

d) -1

Ans d ) -1