Answer :
Answer:
[tex]\left \{ 0,3,6,9,12 \right \}=\left \{ x;x=3n\,,\,n\,\varepsilon \,W ;\,\,n\leq 4\right \}\\\left \{ -3,-2,-1,0,1,2,3 \right \}=\left \{ x;x=\pm n;\,\,n=0,1,2,3 \right \}\\\left \{ m,n,o,p \right \}=\left \{ x;x \,\,is\,\,an\,\,alphabet\,\,after\,\,l\,\,and\,\,before\,\,q \right \}[/tex]
Step-by-step explanation:
The set is a well-defined collection of objects.
Set builder form describes the set by stating the property of each of its elements.
a)
[tex]\left \{ 0,3,6,9,12 \right \}=\left \{ x;x=3n\,,\,n\,\varepsilon \,W ;\,\,n\leq 4\right \}[/tex]
W is a set of whole numbers.
b)
[tex]\left \{ -3,-2,-1,0,1,2,3 \right \}=\left \{ x;x=\pm n;\,\,n=0,1,2,3 \right \}[/tex]
c)
[tex]\left \{ m,n,o,p \right \}=\left \{ x;x \,\,is\,\,an\,\,alphabet\,\,after\,\,l\,\,and\,\,before\,\,q \right \}[/tex]
The set builder notations are:
[tex]\{x : x = 3n; n \to W; n \le 4\}[/tex]
[tex]\{x : x = \pm n; 0 \le n \le 3\}[/tex]
[tex]\{x : x = Alphabet\ A\ ; m \le A \le p\}[/tex]
Set (a): {0,3,6,9,12}
The above set represent whole numbers with a multiple of 3, not greater than 12.
So, the set builder notation is
[tex]\{x : x = 3n; n \to W; n \le 4\}[/tex]
Set (b) {−3,−2,−1,0,1,2,3}
The above set represents integers from -3 to 3
So, the set builder notation is
[tex]\{x : x = \pm n; 0 \le n \le 3\}[/tex]
Set (c) {m,n,o,p}
The above set represents alphabets from m to p
So, the set builder notation is
[tex]\{x : x = Alphabet\ A\ ; m \le A \le p\}[/tex]
Read more about set builder notations at:
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