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

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

2. Every rational number is also a

natural numberwhole numberreal numberinteger

3. 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?

50453060

4. If A ∪ B = ϕ then

A = B = ϕB = ϕA ⊆ BA = ϕ

5. Which one of the following statements is true?

(A - B) ∩ (B - A) ≠ B(A - B) ∩ (B - A) = ϕ(A - B) ∩ (B - A) ≠ A(A - B) ∩ (B - A) = ∪

6. (A’)’ is equal to

∪ϕAA’

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

{0}∪ϕ{0, 2, 3, 4, 5}

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

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

9. 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)

10. Which number has no reciprocal in the set of fractional numbers

-10none of these1

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

ϕ{7, 8}{2, 7, 8}{2}

12. 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}{e,g}ϕ

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

A ⊆ B and B ⊆ AA ‘⊆ BA ⊆ BB ⊆ A

14. The number of subsets of an empty set is

3021

15. 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 = EE ⊆ SS ⊆ ES ≠ E

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

20523540

17. 6x2 - x - 2 > 0, x ∈ R implies

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

4n23n2n

19. 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}{3, 4, 5, 6}ϕnone of these

20. A ∩ ϕ = ϕ if

A = ∪ none of theseA = ϕ true for all A

21. If A ⊆ B and B ⊆ A, then

A ∪ B = ϕB = ϕA = BA = ϕ

22. 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}

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

RR+Q+Z+

24. Which one of the following statements is correct?

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

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

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