Given, S= {1,2,3,4}, state which of the following is a relation on S.a

1.	Given, S= {1,2,3,4}, state which of the following is a relation on S.a) R1= {(1,2),(2,0),(3,1)}b) R2= {(1,3),(4,2),(2,4),(1,4)}C) R3= {(1,1),(1,2),(1,3),(1,4)}d) R4= {(1,2),(0,2),(5,1),(3,2)}
Answer» 1) ∵ (2, 0) ∈ R₁ but 0 \(\notin\) S ∴ R₁ is not a relation on S 2) domain of R₂ = {1, 2, 4} ⊂ S Range of R₂ = {2, 3, 4} ⊂ S Thus, R₂ is a relation on S. 3) domain of R₃ = {1} ⊂ S Range of R₃ = {1, 2, 3, 4} ⊂ S Thus, R₃ is a relation on S. 4) ∵ (0, 2) ∈ R₄ but 0 \(\notin\) S Thus, R₄ is not a relation on S.

Given, S= {1,2,3,4}, state which of the following is a relation on S.a) R1= {(1,2),(2,0),(3,1)}b) R2= {(1,3),(4,2),(2,4),(1,4)}C) R3= {(1,1),(1,2),(1,3),(1,4)}d) R4= {(1,2),(0,2),(5,1),(3,2)}

Answer»

1) ∵ (2, 0) ∈ R₁ but 0 \(\notin\) S

∴ R₁ is not a relation on S

2) domain of R₂ = {1, 2, 4} ⊂ S

Range of R₂ = {2, 3, 4} ⊂ S

Thus, R₂ is a relation on S.

3) domain of R₃ = {1} ⊂ S

Range of R₃ = {1, 2, 3, 4} ⊂ S

Thus, R₃ is a relation on S.

4) ∵ (0, 2) ∈ R₄ but 0 \(\notin\) S

Thus, R₄ is not a relation on S.

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Given, S= {1,2,3,4}, state which of the following is a relation on S.a) R1= {(1,2),(2,0),(3,1)}b) R2= {(1,3),(4,2),(2,4),(1,4)}C) R3= {(1,1),(1,2),(1,3),(1,4)}d) R4= {(1,2),(0,2),(5,1),(3,2)}

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