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Representation of Point on the Plane

If X= 1, 2,...

Question

If $X = {1, 2, 3, 4, 5}$ and $Y = {1, 3, 5, 7, 9}$ determine which of the following sets are (i) mappings (ii) relations (ii) neither of X to Y.
(a) $R_{1} = (x, y) : y = x + 2, x \in X, y \in Y$
(b) $R_{2}$ $= {(1, 1), (2, 1), (3, 3), (4, 3), (5, 5)}$
(c) $R_{3}$ $= {(1, 1), (1, 3), (3, 5), (3, 7), (5, 7)}$
(d) $R_{4}$ $= {(1, 3), (2, 5), (4, 7), (5, 9), (3, 1)}$

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Solution

$i)$ mappings
$(b), (d)$
$i i)$ relations
$(c)$
$i i i)$ neither
$(a)$

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Similar questions

X = {1, 2, 3, 4, 5}, Y = {1, 3, 5, 7, 9},

X

Y

X = {1, 2, 3, 4, 5}

Y = {1, 3, 5, 7, 9}

X \to Y

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}

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

X = {1, 2, 3, 4, 5}

Y = {1, 3, 5, 7, 9}

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