Let A = {1,2,3} , B = {a,b,c,d} be two sets and let R = {(1,a),(1,c),(2,d),(2,c)} be a relation from A to B.Find R^{-1}?

(A)

{(1,a),(1,b),(1,d)}

(B)

{(a,1),(c,1),(d,2),(c,2)}

(C)

{(a,1),(1,c),(d,2),(c,2)}

(D)

{(a,1),(c,1),(2,d),(2,c)}

Question-2

Let A = {1,2,3} ,B = {a,b,c,d} be two sets and let R = {(1,a),(1,c),(2,d),(2,c)} be a relation from A to B.The domain of R is

(A)

{a,b,c,d}

(B)

{1,2}

(C)

{1,2,3}

(D)

{a,b,c,d}

Question-3

Let A = {1,2,3}, B = {1,3,5}.If relation R from A to B given by {(1,3) (2,5), (3,3)} then R^{-1} is.

(A)

{(3,3),(3,1),(5,3)}

(B)

{(1,3),(2,5),(3,3)}

(C)

{(1,3),(5,2)}

(D)

{(3,1),(5,2),(3,3)}

Question-4

Let A and B be two non-empty sets having n elements in common,then A × B and B × A have ___________ elements in common.

(A)

n^{2}

(B)

n

(C)

n/2

(D)

2 n

Question-5

If A × B = {(a,x),(a,y),(b,x),(b,y)}.Find A and B?

(A)

A = {a,b}

B = {x,y}

(B)

A = {a,x}

B = {b,y}

(C)

A = {x,y}

B = {a,b}

(D)

None of these

Question-6

The relation R defined on the set A = {1,2,3,4,5} by R = {(x,y) : < 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

Question-7

If R = {(x,y) : x,y z,x^{2} + y^{2} ≤ 4} is a relation in Z,then domain of R is .

(A)

{0,1,2}

(B)

{-2,-1,0}

(C)

{-2,-1,0,1,2}

(D)

None of these

Question-8

The relation R defined by R = {(x,x+5) : x {0,1,2,3,4,5}.The range of R is

(A)

{1,2,3,4,5}

(B)

{6,7,8,9,10}

(C)

{5,6,7,8,9}

(D)

{5,6,7,8,9,10}

Question-9

A = {1,2,3,4,5} and B = {4,6,9}. A relation R from A to B defined by R = {(x,y) : the difference between x and y is odd, x A,y B}.Write R in Roster form.

(A)

{(1,4) (1,6) (2,9),(3,4) ,(3,6) (5,4), (5,6)}

(B)

{(4,1),(6,2),(9,3),(4,3),(6,3),(4,5),(6,5)}

(C)

{(1,4),(2,6 ) (2,9),(3,4) (3,6),(5,4) (5,6)}

(D)

None of these

Question-10

Let R be a relation in N defined by R = {(1+x,1+x^{2}) : x ≤ 5,x N}.Which of the following is false?

(A)

R = {(2,2),(3,5),(4,10),(5,17),(6,26)}

(B)

Domain of R = {2,3,4,5,6}

(C)

Range of R = {2,5,10,17,26}

(D)

Atleast one is false

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