 # 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:
$$\displaystyle{A}={\lbrace}$$
$$\displaystyle{B}={\lbrace}$$
$$\displaystyle{C}={\lbrace}$$
c. Determine the probability of each of the following:
$$\displaystyle{I}.{P}{\left({C}\right)}$$
$$\displaystyle{I}{I}.{P}{\left({A}\cup{B}\right)}$$
$$\displaystyle{I}{I}{I}.{P}{\left({A}\cap{B}\cap{C}\right)}$$
$$\displaystyle{I}{V}.{P}{\left({B}{C}\right)}$$
$$\displaystyle{V}.{P}{\left({\left({A}{B}\right)}\cap{C}\right)}$$

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself. escumantsu
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,
$$\displaystyle{S}_{{{1}}}=$$ factors of 64 i.e. 1,2,4,8,16,32,64
$$\displaystyle{S}_{{{2}}}=$$ prime numbers
$$\displaystyle{S}_{{{3}}}=$$ multiple of 3
Now describe the sets in words,
$$\displaystyle{S}_{{{1}}}={\left\lbrace{x}:{x}\right.}$$ is a factor of 64 and $$\displaystyle{20}\leq{x}\leq{60}\rbrace$$
$$\displaystyle{S}_{{{2}}}={\left\lbrace{x}:{x}\right.}$$ is prime and $$\displaystyle{20}\leq{x}\leq{60}\rbrace$$
$$\displaystyle{S}_{{{3}}}={\left\lbrace{x}:{x}\right.}$$ is multiple of 3 and $$\displaystyle{20}\leq{x}\leq{60}\rbrace$$
Solution (b).
List of the elements
$$\displaystyle{S}_{{{1}}}={\left\lbrace{32}\right\rbrace}$$
$$\displaystyle{S}_{{{2}}}={\left\lbrace{23},{29},{31},{37},{41},{43},{47},{53},{59}\right\rbrace}$$
$$\displaystyle{S}_{{{3}}}={\left\lbrace{21},{24},{27},{30},\ldots,{57},{60}\right\rbrace}$$
Solution (c).
Determine the probability
Since we have from the b part, $$\displaystyle{S}_{{{1}}}\cup{S}_{{{2}}}={\left\lbrace{32},{23},{29},{31},{37},{41},{43},{47},{53},{59}\right\rbrace}$$
$$\displaystyle{S}_{{{1}}}\cap{S}_{{{2}}}\cap{S}_{{{3}}}=\phi$$
$$\displaystyle{I}.{P}{\left({S}_{{{3}}}\right)}={\frac{{{14}}}{{{40}}}}={\frac{{{7}}}{{{20}}}}$$
$$\displaystyle{I}{I}.{P}{\left({S}_{{{1}}}\cup{S}_{{{2}}}\right)}={\frac{{{10}}}{{{40}}}}={\frac{{{1}}}{{{4}}}}$$
$$\displaystyle{I}{I}{I}.{P}{\left({S}_{{{1}}}\cap{S}_{{{2}}}\cap{S}_{{{3}}}\right)}={\frac{{{0}}}{{{40}}}}={0}$$