State whether each of the following ...

NCERT Class XI Mathematics - Relations and Functions - Solutions

Question : 4 of 36

Marks: +1, -0

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, if P = {m, n} and Q = {n, m}

Then P × Q = {(m, n), (m, m), (n, n), (n, m)}.

(ii) True, by the definition of cartesian product.

(iii) True, We have A = {1, 2} and B = {3, 4}

Now, B ∩ f = f \ A × (B ∩ f) = A × ϕ = ϕ.

Go to Question:

Prev Question

Next Question