Question

P and Q are the subsets of a universal set U. If n(p)=45, n(Q)=55, n=90 and n(PUQ) compliment = 15 find a) N(u) b)n(P intersection Q) Plz so step step by step of solution i will mark u brainliest if u do so

Answer 1

Answer:

Given that P and Q are subsets of universal set U.

Also, n(P) = 45, n(Q) = 55, n( P U Q ) = 90 & n[( P U Q )'] = 15

The formula used to calculate universal set is:

n(x) + n(x') = n(U)

where, x is the set and x' is the complement of this set.

According to the question, we are given n ( P U Q ) and n ( P U Q )'

Hence adding both of them we get:

→ 90 + 15 = 105

Hence value of  n(U) = 105.

Coming to 2nd part of the question.

We know the formula for calculating n ( A U B ) is given as:

→ n ( A U B ) = n (A) + n (B) - n ( A ∩ B )

From this we can arrive at the value of n ( A ∩ B ). Hence we get:

→ n ( P ∩ Q ) = n (P) + n (Q) - n ( P U Q )

→ n ( P ∩ Q ) = 45 + 55 - 90

→ n ( P ∩ Q ) = 100 - 90 = 10

Hence value of n ( P ∩ Q ) is 10.

Answer 2

Answer:

10

Step-by-step explanation:

Given n(P ∪ Q) = 40, n(P) = 18, n(Q) = 22  

We know that n(P U Q) = n(P) + n(Q) - n(P ∩ Q)  

So, 40 = 22 + 28 - n(P ∩ Q)  

40 = 50 - n(P ∩ Q)  

Therefore, n(P ∩ Q) = 50 – 40  

= 10  

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