Math

QuestionCari nilai xx jika n(ξ)=52,n(P)=40,n(PQ)=9n(\xi)=52, n(P)=40, n(P \cap Q)=9 dan n(P)=x+7n\left(P^{\prime}\right)=x+7.

Studdy Solution

STEP 1

Assumptions1. The universal set ξ\xi is the union of sets and $Q$. . The number of elements in the universal set $\xi$ is52.
3. The number of elements in set is40.
4. The number of elements in the intersection of sets and $Q$ is9.
5. The number of elements in the complement of set , denoted ', is x+7x+7.

STEP 2

First, we need to understand that the number of elements in the universal set ξ\xi is the sum of the number of elements in set , set $Q$, and the intersection of sets and QQ. This can be expressed asn(ξ)=n(P)+n(Q)n(PQ)n(\xi) = n(P) + n(Q) - n(P \cap Q)

STEP 3

We also know that the number of elements in the universal set ξ\xi is also the sum of the number of elements in set and its complement $'$. This can be expressed asn(\xi) = n(P) + n(P')$$

STEP 4

Substitute the given values into the equation from3.
52=40+n(P)52 =40 + n(P')

STEP 5

Rearrange the equation to solve for n(P)n(P').
n(P)=5240n(P') =52 -40

STEP 6

Calculate the value of n(P)n(P').
n(P)=5240=12n(P') =52 -40 =12

STEP 7

We know that n(P)=x+7n(P') = x +7. Substitute the value of n(P)n(P') into this equation.
12=x+712 = x +7

STEP 8

Rearrange the equation to solve for xx.
x=127x =12 -7

STEP 9

Calculate the value of xx.
x=127=5x =12 -7 =5The value of xx is5.

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