Set theory is a branch of mathematical logic that studies sets, which are collections of objects. Set theory is concerned with sets that are relevant to mathematics as a whole. Here are some definitions from set theory: Subset: If every element of is also an element of , then is a subset of. Proper subset: If is a subset of and contains something that does not contain. Equality: If and only if for any.  Set theory provides fundamental theoretical structures for other areas of mathematics.  Some concepts in set theory include: Union: The union of two sets A and B contains all the... Show more

Set theory is a branch of mathematical logic that studies sets, which are collections of objects. Set theory is concerned with sets that are relevant to mathematics as a whole.
Here are some definitions from set theory:
Subset: If every element of is also an element of , then is a subset of.
Proper subset: If is a subset of and contains something that does not contain.
Equality: If and only if for any. 

Set theory provides fundamental theoretical structures for other areas of mathematics. 

Some concepts in set theory include:
Union: The union of two sets A and B contains all the objects that are in either set.
Intersection: The intersection of two sets A and B contains all the objects that are in both sets.
Complementation: The complement of set A consists of all the elements that are in the universal set U but not in A. 

Relations can be represented by sets of ordered pairs (a, b) where a bears a relation to b. For example, calendar years may be paired with automobile production figures, weeks with stock market averages, and days with average temperatures

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Math Practice Test: Set Theory

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25 Questions

1. Let A and B be two sets, then n(a) + n(b) equals to

n(A ∩ B)n(A ∪ B) + n (A ∩ B)n(A ∪ B)n(A ∪ B) + n (A ∩ b)

2. If A ⊆ B and B ⊆ A, then

A ∪ B = ϕA = BB = ϕA = ϕ

3. If A = {3, 4, 5, 6} B = { 3, 4, 5, 6, 7} C = {4, 5, 6, 7, 8}, then the value of (A ∩ B) ∪(A ∩ C) is

{5}none of these{3, 4, 5, 6}ϕ

4. For what value of x∈R, 7 - 3x < -4x + 9 is true?

x > -2x > 3x < -3x < 2

5. If n(A) = 20, n(B) = 25, n(A ∩ B) = 10, then find n(A ∪ B)

52203540

6. Which one is the set of all positive rational numbers?

Q+R+RZ+

7. In a group of 1000 people, 700 can read Hindi only and 240 can read English only. How many can read both Hindi and English?

60304550

8. If sets S and E are defined as follows
S = {(x, y):|x - 3| < 1and |y - 3| < 1}
E = {(x, y):4x2 - 9y2 - 32x - 54y -109 = 0}, then

S ⊆ ES = EE ⊆ SS ≠ E

9. Find the solution set of the inequality given by

{x:3 ≤ x ≤ -3, x∈I}{x:3 ≥ x ≥ -3, x∈I}{x: ≤ x ≤ 3, x∈I}{x: ≥ x ≥ -3, x∈I}

10. The number of subsets of an n element set is

2n3n4n2

11. Two sets A and B are equal if and only if

B ⊆ AA ⊆ BA ‘⊆ BA ⊆ B and B ⊆ A

12. Every rational number is also a

whole numberreal numbernatural numberinteger

13. There are 60 students in a class. Each student is offered Art or Sanskrit or both. 35 offered Sanskrit, 20 offered Art and Sanskrit, how many students offered Art only?

45302536

14. (A’)’ is equal to

ϕAA’∪

15. Which one of the following statements is correct?

(A ∪ B)’ = A ∪ B(A ∪ B)’ = A ∪ B’(A ∪ B)’ ≠ A’ ∩ B’(A ∪ B)’ = A’ ∩ B’

16. Find the solution set of the inequality given by <>3|X<>| +<> 4 ><> 22

{x:- 6 > x >6}{x:- 2 < x < 3}{x:- 4 < x < 6}{x:- 3 > x >3}

17. If A = {a, b, c, d},B = {a, e, g},C = { e, g, m, n, p}, find (A ∪ B)∩(A ∪ C)?

none of these{a, b, c, d, e, g}ϕ{e,g}

18. Which of the following sets are different from others (i) ϕ,(ii) {0},(iii) {ϕ}

(i) and (iii) are different from (ii)all are similareach is different from other(ii)

19. 6x2 - x - 2 > 0, x ∈ R implies

20. A ∩ ϕ = ϕ if

A = ϕ true for all Anone of theseA = ∪

21. If ∪ = {0, 1, 2, 3, 4, 5}
A = {1, 2, 3}
B = {0, 2, 3, 5} then the value of (∪ - A) ∪ B is

{0}{0, 2, 3, 4, 5}∪ϕ

22. If A = {2, 4, 5, 7, 8, 9}, B = {2, 7, 6, 8} then the value of A ∩ B is

{2}{7, 8}{2, 7, 8}ϕ

23. If |2x + 1|> 3, x ∈R, then the solution set is given by

{2x:4 >x > 1, x ∈R}{x: > x > 1, x ∈R}{x:2 > x > 1, x ∈R}

24. How many elements are there in the power set of a set having 5 objects?

32684

25. The union of sets A and A’ is denoted by

AϕA’∪ .