Question

if n (AUB)=9 then the number of elements common to each of the sets A×B and B×A is k the sum ofdigit in k bro ans​

Answer 1

Answer:

9

Step-by-step explanation:

Actually nothing can be concluded from the question you have written. But I think you meant $n(A \cap B) = 9$

If that's the case, then the question can be solved.

We have to find $n((A \times B) \cap (B \times A))$

Recall that $n((A \times B) \cap (C \times D)) = n((A \cap C) \times (B \cap D))$

Thus, $n((A \times B) \cap (B \times A)) = n((A \cap B) \times (B \cap A))$

$n((A \cap B) \times (B \cap A)) = 9 \times 9 =81$

Sum of digits = 8 + 1 = 9