Question

State whether each of the following statements is true or false. If the statement is false, rewrite the given statement correctly.

(i) If P = {m, n} and Q = {n, m}, then $P\times Q=$ {(m, n), (n, m)}

(ii) If A and B are non-empty sets, then $A\times B$ is a non-empty set of ordered pairs (x, y) such that $xϵA$ and $yϵB.$

(iii) If A = {1, 2}, B = {3, 4}, then $A\times (B\cap \varphi )=\varphi$

Answer 1

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

Number of elements in set P = 2

Number of elements in set Q = 2

Number of elements in $P\times Q=2\times 2=4$

But $P\times Q=\left\{\right(m,n),(n,m\left)\right\}$ (Given)

Here the statement is false.

So $P\times Q=\left\{\right(m,n),(m,m),(n,n),(n,m\left)\right\}$

(ii) The statement is true.

(iii) The statement is true.