State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly
(i) If P = {m, n} and Q = { n, m}, then P × Q = {(m, n),(n, m)}
(ii) If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ A and y ∈ B
(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ φ) = φ

Solution:

(i) False,

⇒ P x Q = {(m, n), (m, m), (n, n), (n, m)}

(ii) True

(iii) True

NCERT Solutions Class 11 Maths Chapter 2 Exercise 2.1 Question 4

State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly. (i) If P = {m, n} and Q = { n, m}, then P × Q = {(m, n),(n, m)}. (ii) If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ A and y ∈ B. (iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ φ) = φ

Summary:

Three statements are given. We have found that the first statement is false and the other two statements are true