I truefalse1nbsp a b if and only if b isin a and a isin

Assignment Help Applied Statistics

Reference no: EM13371425

I. True/False

1. A = B if and only if B ∈ A and A ∈ B.

2. A ∩ (B ? C) = (A ? B) ∩ (A ? C)

3. (A^c)^c = A

4. B ∩ B^c = Ø

5. If A and B are two sets that are not disjoint, then n(A ? B) = n(A) + n(B).

6. If x ∈ (A ∪ B), then x ∈ A and x ∈ B.

7. If x ∈ A and A ⊂ B, then x ∉ B.

8. If B = {1}, then the subsets of B include {1) and {Ø}.

II. Multiple Choice

10. If x ⊂ (C ∪ D) then it is possible that

a. x ∈ C but x ∉ D

b. x ∈ C^c

c. x ⊂ C^c

d. x ∉ D and x ∉ C

III. Matching

11. e

For disjoint sets, n(A ∪ B) = n(A) + n(B)

12. a

For not disjoint sets, n (A ∪ B) = n(A) + n(B) - n(A ∩ B)

IV. Fill in the Blank

13. __________________ notation is the standard notation to use when denoting sets (such as A = {1, 2, 3}), but ___________________________ notation is just as effective, although it does not require more writing.

14. When two sets have nothing in common they are said to be __________________, which is denoted by n(A ∩ B) = __________________________________.

15. If there are 3 ways of performing task T and 2 ways of performing task Q, then I can determine that there are ____ number of ways of performing task T followed by task Q using the ______Principle.

V. Short Answer

16 b. Consider the new universal set U with subsets C and D, where n(U) = 250, n(C) = 120, n (C ∪ D) = 130, and n(C ∩ D) = 60. Answer the following:

i. What is n(C^c)?

ii. What is n(D)?

iii. What is n(D^c)?

iv. Draw all of this using Venn Diagrams. Be sure to indicate n(U), n(C), n(D), and n(C ∩ D) in your illustration.

Using three circle Venn Diagrams (with the universal set U and subsets A, B, and C), shade the portion that corresponds to the following:

17 b. (A ∩ B^c) ∪ C

18. Let U= {5,10,15,20} and let A = {5,15,20}, B = {5,10,15}, and C = {5, 20}. Answer the following questions:

a. What are all of the subsets of U? List them all.

b. List the elements of the set (C ∪ B^c).

c. List the elements of (A ∩ C)^c.

d. List the elements of A^c ∪ (B ∩ C)^c.

e. Regarding the subsets A, B, and C, which is a subset of the other? Please show using proper notation.

Reference no: EM13371425

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