0070-MWALA_LEARN-SET-THEORY-SOLVING-FOREVER-2

Objectives: Set Theory Questions

Set Theory Questions

Answer the following questions:

1. If A = {a, b, c}, which of the following statements are true?

(a) a ∈ A

(b) de ∈ A

(c) e ∈ A

(d) b ∈ A

2. If A = {a, b, c, d} which of the following statements represent set A?

(a) A set of four letters of the English alphabet.

(b) Some of the sets of the first four letters of the English alphabet.

(c) The set of the first four letters of the English alphabet.

(d) The set of the four consonants of the English alphabet.

3. Describe the following set in words A = {1, 4, 9, 16, 25}

4. List the elements of the set given by A = {x : x is a counting number < 8}

5. Which of the following sets is an empty set?

(a) A = {∅}

(b) B = {0}

(c) R = ∅

(d) S = { }

6. Which of the following sets are equal or equivalent?

A = {1, 2, 3, 4, 5}

B = {1, 4, 7, 10, 15}

C = {cars, ships, aeroplanes}

D = {cars, ships, aeroplanes}

7. Which of the following sets are finite or infinite?

A = {x : x is a prime number}

B = {all letters of the English alphabet}

C = {all students in your school}

D = {1, 4, 9, 16, ...}

E = {1, 4, 9, 16, 25, ..., 81}

8. If A = {a, b} show by using symbols that a and b are elements of A.

9. How many subsets are there in A = {a, b, c, d, e, f, g}?

10. List all the subsets of A = {2, 4, 6}

11. In the following pairs of sets name the set which is a subset of the other:

(a) A = {a, b, c} and B = {e, d, b, c, a}

(b) C = {Tom, John, Idrisa} and D = {John, Tom}

12. If A = {a, b, c}, B = {4, a, 1} and D = {b, a, 1} which of the following statements are true?

(a) A ⊂ B

(b) B ⊂ D

(c) A ⊂ D

(d) D ⊂ A

13. If A = {a, b, c, d} and B = { } find:

(a) A ∪ B

(b) A ∩ B

14. Let A be the set of the first ten counting numbers and B be the set of the first four prime numbers. Find:

(a) A ∪ B

(b) A ∩ B

15. If U = {1, 2, 3, 4, 5} and A = {2, 3, 5} list the elements of A′.

16. If U = {a, b, c, d, e}, B = {d, e} and A = {a, b, c} find the following:

(a) A′ ∩ B′

(b) A ∪ (B ∩ A)

17. Draw a Venn diagram and show by shading the region representing each of the following:

(a) A ∪ B

(b) B′ ∩ A′

(c) (A ∩ B)′

(d) U \ (A′ ∩ B′)

18. In a group of 29 tourists from different countries, 17 went to Manyara National Park, 13 went to Mikumi National Park and 8 went to neither Mikumi nor Manyara National Park. How many tourists went to both places?

Answer the following questions:

19. Show by a Venn diagram that A′ ∪ A = U. Shade the required region.

20. Consider the following figure and answer the questions that follow.

[Two intersecting circles showing sets A and B with elements inside.]

(a) List the members of set A

(b) List the members of set B

(c) Find n(A ∪ B)

21. In a certain street with 200 houses, 170 houses have electricity and 145 houses have glass doors. How many houses have both electricity and glass doors? Assuming that each house has either a glass door or electricity or both.

22. In an interview at a railway station, 50 travelers reported that last month they had been to Tanga, 48 had been to Arusha and 36 had been to both Arusha and Tanga. How many travelers were interviewed?

Reference Book: N/A

Author name: SIR H.A.Mwala Work email: biasharaboraofficials@gmail.com
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