Question

Q.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.

No spam
Irrelevant answers will be reported on spot ​

Answer 1

Answer:

(i) Given P={m,n} and Q={n,m} then

P×Q={(m,n),(m,m),(n,n),(n,m)}

So, given value of P×Q is incorrect.

Hence, the given statement (i) is false.

(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

Hence, the given statement (ii) is true.

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

A×(B∩ϕ)=A×ϕ=ϕ

So, (iii) is true.

Step-by-step explanation:

i hope it was help for you

Answer 2

$\huge\bold{\underline{\underline{{Question:}}}}$

Q.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.

$\huge\bold{\underline{\underline{{Answer:}}}}$

(i) Given P={m,n} and Q={n,m} then

P×Q={(m,n),(m,m),(n,n),(n,m)}

So, given value of P×Q is incorrect.

Hence, the given statement is false.

(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

Hence, the given statement is true.

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

A×(B∩ϕ)=A×ϕ=ϕ

So, it is true.