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Definition of Relations

If A = a, b, ...

Question

If A = {a, b, c, d}, B={1, 2, 3}, find whether or not the following sets of ordered pairs are relations from A to B or not
(a) $R_{1}$ ={(a, 1), (a, 3)}
(b) $R_{2}$ = { (b, 1), (c, 2), (d, 1)}
(c) $R_{3}$ = {(a, 1), (b, 2),( 3, c)}

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Solution

$R_{1}$ and $R_{2}$ are relations as both are subsets of $A \times B$ but $R_{3}$ is not a relation from A to B as the ordered pair (3, c) $\in B \times$ A and $\notin A \times B$

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Similar questions

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)} .

Which of the following are relations from the set $A = {1, 2, 3, 4}$ to set $B = {a, b, c}$ ?

A = 1, 2, 3, 4, 5

B = 1, 3, 5, 7, 9, 10, 17, 26, 30 .

R_{1}

R_{2}

R_{3} = (x, y) : x \in A, y \in B, x + y = 8

R_{4} = (x, y) : x \in A, y \in B, y = x^{2} + 1

R_{5} = (x, y) : x \in A, y \in B, y = 2 x - 1

A = {1, 2, 3, 4, 5}, B = {1, 3, 5, 7, 9, 10, 17, 26, 30}

R_{1} = {(1, 3), (3, 3), (5, 17), (1, 2)}

R_{2} = {(3, 7), (4, 5), (5, 30)}

R_{3} = {(x, y) : x ϵ A, y ϵ B, x + y = 8}

R_{4} = {(x, y) : x ϵ A, y ϵ B, y = x^{2} + 1}

R_{5} = {(x, y) : x ϵ A, y ϵ B, y = 2 x - 1}

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