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Q.

Let X = {1,2,3, 4, 5, 6} and Y = {1,3,5,7,9}. Which of the following is/are relations from X to Y?

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a

R1=(x,y):y=2+x,x∈X,y∈Y

b

R2=(1,1),(2,1),(3,3),4,3,5,5

c

R3=(1,1),(1,3),(3,5),3,7,5,7

d

R4={(1,3),(2,5),(2,4),7,9

answer is B.

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Detailed Solution

X = {1,2,3, 4,5} Y = {1,3, 5, 7, 9}(a). R1={(x,y):y=2+x,x∈X,y∈Y}     x=1  y=3x=2  y=4x=3  y=5x=4  y=6x=5  y=7So, R is not a relation from X to Y. (b).      R2={(1,1),(2,1),(3,3)(4,3),(5,5)} R2⊆X×Y(c).      R3={(1,1),(1,3),(3,5)3,7(5,7)} R3⊆X×Y(d). R4⊈X×Y
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