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If A = {1, 2}, B = {3, 4} and C ={x : x is even x divides 15}, that show that

$space space space space straight A space straight x space left parenthesis straight B intersection straight C right parenthesis space equals space straight ϕ$

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7.
State whether each of the following statements are True or False. If the statement is False, re-write it correctly.

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

(ii) If A and B are two non-empty sets, then A x B is a non-empty set of ordered pairs (x, y) such that $space space space space straight x element of straight B space and space straight y element of straight A$ .

(iii) If A = {1, 2}, B = {3, 4}, then $space space space space space space space space space space straight A space cross times left parenthesis straight B intersection straight ϕ right parenthesis equals straight ϕ$

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

$rightwards double arrow$ n(P|) = 2, n(Q) = 2

$rightwards double arrow$ n(P xQ) =n(P) x n(Q) = 2 x 2 = 4

But, it is given that P x Q = {(m, n).(n, m)}

$rightwards double arrow$ n(P x Q) = 2

Hence, the statement is False.

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

(ii) The statement is False. The correct statement is $space space space space space space space space space space space straight A cross times straight B equals left curly bracket left parenthesis straight x comma space straight y right parenthesis space colon space straight x element of straight A comma space straight y element of straight B right curly bracket$

(iii) The statement is true as $space space space space space space space space space space space space straight A cross times left parenthesis straight B intersection straight ϕ right parenthesis space equals space left curly bracket 1 comma space 2 right curly bracket space straight X space left square bracket left curly bracket 3 comma space 4 right curly bracket intersection straight ϕ right square bracket space equals space left curly bracket 1 comma space 2 right curly bracket space cross times straight ϕ space space space space open square brackets space because space straight B intersection straight ϕ equals straight ϕ close square brackets$

$space space space space space space space space space space space space space space space space space space space space space open square brackets because space space straight A space cross times space straight ϕ close square brackets space equals space straight ϕ$