Question

if n(AxB)=15,A and B are not Singleton sets and A subset B then n(A)=___ and n(B)=____​

Answer 1

Answer:

as sets are not singleton than only two combinations are possible either n(A)=3 and n(B)=5 or vice versa

Answer 2

answer : n(B) = 7

explanation :

☁️ A and B are not singleton sets. That is they have more than one element.

☁️ that is, both sets have more than 2^1 = 2 subsets

☁️ Now it is given that n(A×B) = 21

    ie., n(A) * n(B) = 21

☁️ it is also given that A is a subset of B. Therefore n(A) < n(B).

☁️ okay now we gotta find n(A) and n(B).

    well what are the possible pairs of factors of 21? They are 1,21 and 3,7.

as I’ve said in the 2nd line sentence, A and B should have more than 2 subsets. So the only possible pairs are 3,7.

therefore n(A) = 3 and n(B) = 7