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

{e,g}ϕ{a, b, c, d, e, g}none of these

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

ϕ{0}{0, 2, 3, 4, 5}∪

3. A ∩ ϕ = ϕ if

A = ∪ A = ϕ true for all Anone of these

4. Find the solution set of the inequality given by

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

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

0none of these1-1

6. 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?

45253630

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

Q+Z+R+R

8. Every rational number is also a

whole numberreal numbernatural numberinteger

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

43286

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

A’ϕA∪ .

11. (A’)’ is equal to

A’A∪ϕ

12. Which one of the following statements is true?

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

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

{2, 7, 8}ϕ{2}{7, 8}

14. If A ∪ B = ϕ then

A = B = ϕA ⊆ BA = ϕB = ϕ

15. If A ⊆ B and B ⊆ A, then

B = ϕA ∪ B = ϕA = BA = ϕ

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

52352040

17. 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

ϕ{5}{3, 4, 5, 6}none of these

18. 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

19. 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 ⊆ ES ≠ EE ⊆ S

20. The power set of {0} is

ϕ{ϕ, {0}}{ϕ}{0}

21. 6x2 - x - 2 > 0, x ∈ R implies

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

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

23. 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)

24. 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}

25. A ∪ B = A if

B = ϕA = ϕA ⊆ BB ⊆ A