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Question

# Let A={x:x∈Z,|x|≤3} and B={y;y∈N,−1<y+2≤4}. If R be the relation from A to B, then

A
Co domain of R is {1,2}
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B
Range of R is {0,1,2}
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C
R1 can be {(1,1),(1,2),(1,3),(2,1),(2,2),(2,3)}
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D
Co domain of R1 is {3,2,1.0,1,2,3}
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Solution

## The correct option is D Co domain of R−1 is {−3,−2,−1.0,1,2,3}Here, A={x:x∈Z,|x|≤3} |x|≤3 ⇒−3≤x≤3 Since, x∈Z A={−3,−2,−1,0,1,2,3} B={y;y∈N,−1<y+2≤4} −1<y+2≤4 ⇒−3<y≤2 Since, y∈N B={1,2} Here, R is a relation from A to B ∴ Codomain of R is B={1,2} Since Range of a relation is ⊂ of Co domain Range ≠{0,1,2} R−1 will be a relation from B to A R−1⊂B×A ∴R−1 can be {(1,1),(1,2),(1,3),(2,1),(2,2),(2,3)} ∴ Codomain of R−1 is A={−3,−2,−1,0,1,2,3}

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