 # The Universal Set, U, consists of the natural numbers from 20 to 60 incluive Define or describe in words the following three (3) sets: factors of 64, prime numbers, and multiples of 3. Anonym 2021-08-09 Answered
The Universal Set, U, consists of the natural numbers from 20 to 60 incluive
a. Define or describe in words the following three (3) sets: factors of 64, prime numbers, and multiples of 3.
b. List the elements in each of your sets:
$A=\left\{$
$B=\left\{$
$C=\left\{$
c. Determine the probability of each of the following:
$I.P\left(C\right)$
$II.P\left(A\cup B\right)$
$III.P\left(A\cap B\cap C\right)$
$IV.P\left(BC\right)$
$V.P\left(\left(AB\right)\cap C\right)$
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Step 1: Given,
The universal set U, consist of the natural numbers from 20 to 60 inclusive. We have to answer the following...
Step 2: Explanation
Solution (a).
If we have 3 sets,
${S}_{1}=$ factors of 64 i.e. 1,2,4,8,16,32,64
${S}_{2}=$ prime numbers
${S}_{3}=$ multiple of 3
Now describe the sets in words,
${S}_{1}=\left\{x:x$ is a factor of 64 and $20\le x\le 60\right\}$
${S}_{2}=\left\{x:x$ is prime and $20\le x\le 60\right\}$
${S}_{3}=\left\{x:x$ is multiple of 3 and $20\le x\le 60\right\}$
Solution (b).
List of the elements
${S}_{1}=\left\{32\right\}$
${S}_{2}=\left\{23,29,31,37,41,43,47,53,59\right\}$
${S}_{3}=\left\{21,24,27,30,\dots ,57,60\right\}$
Solution (c).
Determine the probability
Since we have from the b part, ${S}_{1}\cup {S}_{2}=\left\{32,23,29,31,37,41,43,47,53,59\right\}$
${S}_{1}\cap {S}_{2}\cap {S}_{3}=\varphi$
$I.P\left({S}_{3}\right)=\frac{14}{40}=\frac{7}{20}$
$II.P\left({S}_{1}\cup {S}_{2}\right)=\frac{10}{40}=\frac{1}{4}$
$III.P\left({S}_{1}\cap {S}_{2}\cap {S}_{3}\right)=\frac{0}{40}=0$