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NCERT Exemplar Class 11 Maths Chapter 2 Relations and Functions Exercise Solutions True or False Questions
Table of Contents
Solved True or False Type Questions of NCERT Exemplar Relations and Functions Exercise
State True or False for the following statements in each of the Exercises from 38 to 42 :
Question 38
The ordered pair (5, 2) belongs to the relation
R = {(x, y) : y = x − 5, x, y ∈ Z}
Answer 38
Given that
R = {(x, y) : y = x − 5, x, y ∈ Z}
For (5, 2):
Put x = 5
y = 5 − 5 = 0 ≠ 2
So, (5, 2) is not an ordered pair of R.
Hence, the statement is false.
Question 39 If P = {1, 2}, then
P × P × P = {(1, 1, 1), (2, 2, 2), (1, 2, 2), (2, 1, 1)}
Answer 39
Given that
P = {1, 2}
∴ P × P = {1, 2} × {1, 2}
= {(1, 1), (1, 2), (2, 1), (2, 2)}
∴ P × P × P
= {(1, 1), (1, 2), (2, 1), (2, 2)} × {1, 2}
= {(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2), (2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)}
So, the given statement is False.
Question 40. If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, then (A × B) ∪ (A × C)
= {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}
Answer 40.
Given that A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}
A × B = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}
A × C = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}
(A × B) ∪ (A × C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}
Hence, the given statement is True
Question 41. If (x − 2, y + 5) = (−2, 1/3) are two equal ordered pairs, then x = 4, y = −14/3.
Answer 41. Given that
(x − 2, y + 5) = (−2, 1/3)
⇒ x − 2 = −2
⇒ x = 0 and
y + 5 = 1/3
⇒ y = 1/3 − 5
⇒ y = −14/3
Hence, the given statement is False.
Question 42. If A × B = {(a, x), (a, y), (b, x), (b, y)}, then
A = {a, b} and B = {x, y}.
Answer 42. Given that
A = {a, b} and B = {x, y}
∴ A × B = {(a, x), (a, y), (b, x), (b, y)}
Hence, the statement is True.