KCET2012MathematicsSets and Relations
If A and B have n elements in common, then the number of elements common to A B and B A is
Options
- An
- B2 n
- Cn ²
- D0
Correct answer
C. n ²
Step-by-step solution
Let C = A B , then C C=(A B) (A B)=(A B) (B A) gathered =(A B) (B A) [ (A C) (B D)=(A B) (C D)] gathered Since, A B has n elements, so C has n elements. Hence, C C has n ² elements. ( A B ) ( B A ) has n ² elements. Hence, A B and B A has n ² elements in common.