Given a relation R = {(x,y) : x > y + 2}. State which of the given ordered pairs belong to this relation.

(3,0)

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(5,4)

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(-7,-10)

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(9,7)

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Solution

The correct options are
A (3,0)
C (-7,-10)
In (3,0) , x = 3 and y = 0. y+2 = 2 which is < x.
In (5,4) , x = 5 and y = 4. y+2 = 6 which is > x.
In (-7,-10) , x = -7 and y = -10. y+2 = -8 which is < x.
In (9,7) , x = 9 and y = 7. y+2 = 9 which is = x.

Hence, (3,0) and (-7,-10) belong to the given relation.

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Similar questions

Q. Let

A = {x : x = 2 n + 1, n \in W}

and

B = {y : y = 2 n, n \in N} .

If a relation

R

is defined from

A

B,

then which of the following is void relation?

Q. Let

A = 1, 2, 3, 4, 5

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

Which of the following sets of ordered pairs are (i) relations (ii) functions (iii) neither, from A to B
(a)

R_{1}

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

R_{2}

= {(3, 7), (4, 5), ( 5, 30)}
(c)

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

(d)

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

(e)

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

Determine whether each of the following relations are reflexive, symmetric and transitive:
(v) Relation R in the set A of human beings in a town at a particular time given by
(a) R = {(x, y): x and y work at the same place}
(b) R = {(x, y): x and y live in the same locality}
(c) R = {(x, y): x is exactly 7 cm taller than y}
(d) R = {(x, y): x is wife of y}
(e) R = {(x, y): x is father of y}