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B.
List the subsets of set Q given that Q={w, x, y, z}.
1. no element
How many such subsets?
2. one element only
How many such subsets?
3. two elements only
How many such subsets?
f).
4. three elements only
How many such subsets?
5. four elements
How many such subsets?
6. Give the total number of subsets of What the answer

Sagot :

DubuChewyidn

SETS

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1. no element, How many such subsets?

[tex]\textcolor{brown}{\mathsf{Subsets \: with \: no \: element:}} \\ \mathsf{Subset}: \(\{\}\) (\mathsf{the \: empty \: set)} \\ \mathsf{Number \: of \: subsets}: 1[/tex]

2. one element only, How many such subsets?

[tex] \textcolor{brown}{\mathsf{Subsets \: with \: one \: element:}} \\ \mathsf{Subsets}: \(\{w\}, \{x\}, \{y\}, \{z\}\) \\ \mathsf{Number \: of \: subsets}: 4[/tex]

3. two elements only, How many such subsets?

[tex]\textcolor{brown}{\mathsf{Subsets \: with \: two \: elements:}} \\ \mathsf{Subsets}: \(\{w, x\}, \{w, y\}, \{w, z\}, \{x, y\}, \{x, z\}, \{y, z\}\) \\ \mathsf{Number \: of \: subsets}: 6[/tex]

4. three elements only, How many such subsets?

[tex]\textcolor{brown}{\mathsf{Subsets \: with \: three \: elements:}} \\ \mathsf{Subsets}: \(\{w, x, y\}, \{w, x, z\}, \{w, y, z\}, \{x, y, z\}\) \\ \mathsf{Number \: of \: subsets}: 4[/tex]

5. four elements, How many such subsets?

[tex]\textcolor{brown}{\mathsf{ \: \: \: \: \: \: \: \: \: Subsets \: with \: four \: elements:}} \\ \mathsf{Subset}: \(\{w, x, y, z\}\) \\ \mathsf{Number \: of \: subsets}: 1[/tex]

6. Give the total number of subsets of What the answer

[tex] \textcolor{brown}{\mathsf{Total \: number \: of \: subsets:}} \\ \mathsf{The \: total \: number \: of \: subsets \: of \: a \: set \: with \: } \( n \) \mathsf{\: elements \: is \: } \( 2^n \). \\ \mathsf{For \: } \( Q \) \mathsf{\: with \: 4 \: elements: \: } \( 2^4 = 16 \) [/tex]

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