Question

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 $space space space space space space space space space space straight A space cross times left parenthesis straight B intersection straight ϕ right parenthesis equals straight ϕ$

Solution

(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 $space space space space space space space space space space space space straight A cross times left parenthesis straight B intersection straight ϕ right parenthesis space equals space left curly bracket 1 comma space 2 right curly bracket space straight X space left square bracket left curly bracket 3 comma space 4 right curly bracket intersection straight ϕ right square bracket space equals space left curly bracket 1 comma space 2 right curly bracket space cross times straight ϕ space space space space open square brackets space because space straight B intersection straight ϕ equals straight ϕ close square brackets$

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

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Trigonometric Functions

Some More Questions From Trigonometric Functions Chapter

If A = {a, b, c} and B = {p, q}, then find :

(i) A x B (ii) B x A (iii) A x A (iv) B x B (v) n (A x B) (vi) n (B x A) (vii) n (A x A) (viil) n (B x B).

If A = {–1, 1}, find A × A × A.

Let A = {–1, 1}, B = {2, 3}, C = {3, 5} be subsets of real numbers.

Let A = {–1, 1}, B = {2, 3}, C = {3, 5} be subsets of real numbers.

n(A X A)

Let A = {–1, 1}, B = {2, 3}, C = {3, 5} be subsets of real numbers.

n(A X A X A)

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