if A andB are two sets thant n(A)=100,n(B)=150and n(A intersection B)=50 find the following values A)n(A union b) B)n(A-B)
this chapter name sets please fast answer me
Answers
Answer:
A and B are two sets such that,
n ( A) = 150
n ( B) = 250
We are also given the value of A ∪ B.
So, Let's look at the formulae we have
n ( A \bigcup B ) = n ( A) + n ( B) - n ( A \bigcap B ) \: \:n(A⋃B)=n(A)+n(B)−n(A⋂B)
So , We will find value of n ( A∩B ) now,
\begin{gathered}300 = 150 + 250 - (A \bigcap B) \\400 - 300 = (A\bigcapB) \\ (A\bigcapB) = 100\end{gathered}
300=150+250−(A⋂B)
400−300=(A\bigcapB)
(A\bigcapB)=100
Now,
Let's look at one more formula,
\begin{gathered}n ( A \bigcup B) = n ( A - B)+ n( B) \\ 300 = n ( A - B) + 250 \\ 300 - 250 = n ( A - B) \\ 50 = n ( A - B)\end{gathered}
n(A⋃B)=n(A−B)+n(B)
300=n(A−B)+250
300−250=n(A−B)
50=n(A−B)
\begin{gathered}n ( A \bigcup B) = n ( A )+ n( B -A) \\ 300 = 150 + n( B -A) \\ 150 = n( B -A)\end{gathered}
n(A⋃B)=n(A)+n(B−A)
300=150+n(B−A)
150=n(B−A)
We have found that,
n ( A - B) = 50
n ( B - A) = 150 .
How do we know if we are correct, We do have a formula to check,
That is,
\begin{gathered}n( A \bigcup B) = n ( A - B ) + n ( B - A) + n(A \bigcap B ) \\ \end{gathered}
n(A⋃B)=n(A−B)+n(B−A)+n(A⋂B)
Substituting the values,
\begin{gathered}300 = 50 + 150 + 100 \\ 300 = 300\end{gathered}
300=50+150+100
300=300
We see both L. H. S and R. H. S are equal, Hence our solution is correct.
\boxed{ Therefore, \: n ( A - B) = 50 , \: < br / > n ( B - A) = 150 }
Therefore,n(A−B)=50,<br/>n(B−A)=150
Answer:
in which exercise 1.6