Solution to List all elements of the following sets as a set. All answers must be exact … - Sikademy
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Archangel Macsika

List all elements of the following sets as a set. All answers must be exact and not rounded 1.{q is an integer | q is a factor of 231} Describe the following sets using proper set-builder notation as explained in your book. You may not simply list the numbers 1. {1, 9, 27, 81, 243, 729} 2. The rational numbers that are strictly between -4.1 and 3.2 3. The negative even integers that are multiples of 7 Let A = {a, b, c, 1, 2, 3, q, r, s}, B = {a, 1, r}, and C = {a, 3, q, x, y, z}. Which of the following statements are true? Which are false? Explain your answers. 1. 3 ∈A 2. z ∈A 3. B ⊂A 4. {1,3}∈A 5. {1,3}⊂A 6. A ⊂A 7. B ⊆B 8. ∅ ⊆C Let A, B, and C be as in #4 and let U = {1, 2, 3, 5, 7, 8, 9, a, b, c, d, e, f, g, x, y, z}. Determine: 1. A ∩B 2. A ∩C 3. A ∪B 4. A ∪C 5. A-B 6. A -C 7. B-A 8. C-A 9. A^C 10 .A⨁C

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1 . Factors of 231 are 1,3,7,11,21,33,77

In set notation,A= {1,3,7,11,21,33,77}

1 . These numbers are in succesive powers of 3.

So,in set builder form,A= {x\in 3^n | 6\geqslant n \geqslant 0 \ \ \& \ n\neq1 }

2 .A={x\in Q|-4.1<x<3.2 }

3 .As the given numbers are negative even numbers,this means they must be divisible by 2,So A= {7n\ | n<0\ \&\ n=0\, mod\, 2 }

4 .Given,A = {a, b, c, 1, 2, 3, q, r, s }. B = {a, 1, r}, and C = {a, 3, q, x, y, z}

1 . Yes 3 \in A

2 . False

3 . {a,1,r} \in A .So,Yes,B ⊂A

4 . False,As we know 1\in A,3\in A but {1,3} does not belong to A.

5 . Yes {{1,3} } as a set is a subset of A .So,{1,3}⊂A

6 . Every set is a not a subset,but a proper subset of itself .Hence,it is not true.

7 . Every set is a proper subset of itself.So,B ⊆B is true.

8 .\phi is a subset of every set.Hence,∅ ⊆C

Let A, B, and C be as in 4 and let U = {1, 2, 3, 5, 7, 8, 9, a, b, c, d, e, f, g, x, y, z}.

1. A ∩B={a,1,r}

2 .A ∩C={a,3,q}

3 .A U B={a, b, c, 1, 2, 3, q, r, s}

4 .A U C={a, b, c, 1, 2, 3, q, r, s,x,y,z}

5 .A-B={ b, c, 2, 3, q,s}

6 .A -C={ b, c, 1, 2, r, s}

7 .B-A=\phi

8 .C-A={x,y,z}

9 .A^c= {5,7,8,9,d,e,f,x,y,z}

10 .A⨁C=(A∩C^c)U(C∩A^c) ={b,c,1,2,r,s,x,y,z}



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Question ID: mtid-5-stid-8-sqid-4036-qpid-2735