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 are
In set notation {}
1 . These numbers are in succesive powers of 3.
So,in set builder form, { }
2 .A={ }
3 .As the given numbers are negative even numbers,this means they must be divisible by 2,So { }
4 .Given, { }. B = {a, 1, r}, and C = {a, 3, q, x, y, z}
1 . Yes
2 . False
3 . {a,1,r} .So,Yes,B ⊂A
4 . False,As we know but {1,3} does not belong to A.
5 . Yes { } 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 . 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=
8 .C-A={x,y,z}
9 . {5,7,8,9,d,e,f,x,y,z}
10 .A⨁C ={b,c,1,2,r,s,x,y,z}