Question

State whether each of the following statements are true or false. If the statement is false, re-write 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 $xϵB$ and $yϵA.$

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

Answer 1

(i) False,

If p = (m, n) and Q = (n, m),

Then,

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

(ii) False

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

(iii) True.