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Definition of Relations

Which of the ...

Question

Which of the following are identity relations of set $A = {1, 2, 3}$
1. $R_{1} = {(1, 1), (2, 2)}$
2. $R_{2} = {(1, 1), (2, 2) (3, 3), (1, 3)}$
3. $R_{3} = {(1, 1), (2, 2), (3, 3)}$

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Solution

The relation $R_{3}$ is identity relation on set $A$ .
$R_{1}$ is not identity relation on set $A$ as $(3, 3) \notin R_{1}$ . $R_{1}$
$R_{2}$ is not identity relation on set $A$ as $(1, 3) \in R_{2}$

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Similar questions

A = {1, 2, 3}

B = {4, 5, 6}

A

B

R_{1} = {(4, 2) (2, 6) (5, 1) (2, 4)}

R_{2} = {(1, 4) (1, 5) (3, 6) (2, 6) (3, 4)}

R_{3} = {(1, 5) (2, 4) (3, 6)}

R_{4} = {(1, 4) (1, 5) (1, 6)}

A = {a, b, c, d}, B = {1, 2, 3}

A

B

R_{1} = {(a, 1), (a, 3)}

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

R_{3} = {(a, 1), (b, 2), (3, c)} .

A = (1, 2, 3}

R_{1}

1

R_{2}

2

A = {5, 7, 9},

A

A = {1, 2, 3}

R_{1} = {(1, 1), (1, 3) (3, 1) (2, 2), (2, 1) (3, 3)}

R_{2} = {(2, 2), (3, 1), (1, 3)}

R_{3} = {(1, 3), (3, 3)}

R_{4} = A \times A .

R_{1}, R_{2}, R_{3}, R_{4},

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