A and B are not Singleton set.n(A×B) =21.If A is subset of B then n(B)=.......
Answers
Therefore n(B) = 7
Step-by-step explanation:
A and B are not singlenton set. n(A×B)= 21
The factor of 21 = 7×3 [ since 7 and 3 both are prime number]
Given A is subset of B.
n(B) = either 7 or 3 and n(A) = either 7 or 3
Since A is subset of B. So, n(B) >n(A)
Therefore n(B) = 7
answer : n(B) = 7
explanation :
☁️ A and B are not singleton sets. That is they have more than one element.
☁️ i.e., both set A and B have more than 2^1 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