Question

If A = {letters of the word CRICKET} and B = {letters of the word HOCKEY}, then A and B are ___.

• A. equal sets
• B. disjoint sets
• C. infinite sets
• D. equivalent sets

Answer 1

The correct option is D

equivalent sets

$A=\left\{\text{Letters of the word CRICKET}\right\}$

$\Rightarrow A=\left\{\text{C, R, I, K, E, T}\right\}$

$\Rightarrow n\left(A\right)=6$

$B=\left\{\text{Letters of the word HOCKEY}\right\}$

$\Rightarrow B=\left\{\text{H,O,C,K,E,Y}\right\}$

$\Rightarrow n\left(B\right)=6$

Thus, $n\left(A\right)=n\left(B\right).$

$\Rightarrow$ A and B are equivalent sets.

A and B are not disjoint as $A\cap B=\left\{\text{C,K,E}\right\}\ne \varphi .$