Q. If $A = \left\{ a,b,\ c \right\},\ B = \{ b,\ c,\ d\}$ and $C = \{ a,\ d,\ c\}$, then $(A - B) \times (B \cap C)$ is equal to
A) $\{(a,\ c),\ (a,\ d)\}$
B) $\{(a,\ b),\ (c,\ d)\}$
C) $\{(c,\ a),\ (d,\ a)\}$
D) $\{(a,\ c),\ (a,\ d),\ (b,\ d)\}$
Explanation
(a)
Given, $A = \left\{ a,\ b,\ c \right\},\ \ \ \ \ \ \ B = \{ b,\ c,\ d\}$ and $C = \{ a,\ d,\ c\}$
Now, $A - B = \left\{ a,\ b,\ c \right\} - \left\{ b,\ c,\ d \right\} = \{ a\}$
And $B \cap C = \left\{ b,\ c,\ d \right\} \cap \left\{ a,\ d,\ c \right\} = \{ c,\ d\}$
$\therefore(A - B) \times (B \cap C) = \{ a\} \times \{ c,\ d\}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \{(a,\ c),\ (a,\ d)\}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.