Elementary Set Theory - Quick Review

Mark each of the following sets as valid or invalid

1. (1) Set of natural numbers.
2. (2) Set of roots of the equation, x²  + 7x + 6 = 0.
3. (3) A set consisting of prime minister of Australia, capital of the United States, natural numbers 1–10, Taj Mahal and alphabets a–c.
4. (4) Set of rich people.
5. (5) Set of cleaver students.

Given the following set expressions, assign the right meaning to each symbol

1. x, y ∊ A
2. A = { x|x is an odd negative number } here -3 ∊ A, 8 ∉ A
3. A = ∅
4. N = {1, 2, 3, 4, ...}, n(N) = ℵ₀
5. R = {points in a plane}, n(R) = c
6. x ∊ A ⇔ x ∊ B 

1. (1) capital letter A
2. (2) small letter x
3. (3) ∊
4. (4) ∉
5. (5) { } (curly brackets)
6. (6) | (pipe)
7. (7) , (comma) between x and y
8. (8) ∅
9. (9) ℵ₀ (aleph-null)
10. (10) c
11. (11) ⇔

 

Let A = { x|x + 5 = 5 }

set A = (1)

Assign the right term for each expression

1. A = ∅ (1)
2. A = {∅} (2)

If a set A contains finite number of elements n, we denote the cardinal number of set A by n(A).  In other words, n(A) stands for the number of elements in a finite set.

What are the cardinal number for each of the following sets?

1. A = {1, 3, 4, 5, 6, 7} (1)
2. B = {a, b, c, d, e, f, g, h} (2)
3. C = {2, 4, 6, 8, 10} (3)

The cardinal number of (1) infinite set, N = {1, 2, 3, 4, ...} (or any other set that is equivalent to N), is denoted by the symbol ℵ₀ (read aleph-null). The symbol “c” is used to denote the cardinal number of an (2) infinite set, like the set of all real numbers or the set of points in an open interval or the set of points in a plane.

What is the cardinal number of the empty set

n(∅) = (1)

Please type a number

Given A = {1, 2, 3, 4, 5}, B = {1, 2, 3}, C = {2, 3, 1}, D = {6, 7, 8}.  Mark true or false for the following

1. A ⊆ B (1)
2. B ⊆ A (2)
3. C ⊆ B (3)
4. B ⊆ C (4)
5. D ⊈ A (5)

The set B is called the (1) of A

The sets A = {1, 2} and B = {1, 2, 3} are (1) as A ⊆ B. On the other hand, the sets C = {1, 2, 3} and D = {2, 3, 4} are (2).

 

∅ has (1) elements

 

A ∪ B = {x|x ∊ A (1) B (2) both}

Let A = {1, 2, 3}, B = {2, 3, 5, 6}, and C = {5, 7, 8}. 

Complete the following intersection operations with the right values

• A ∩ B = (1)
• B ∩ C = (2)
• A ∩ (3) = ∅

Let U be the universal set and A is a proper subset of U, Then

A' = (1)

Let U the universal set, A a proper subset of U

• (A')^' = U - A' = U - ((1)) = A
• ∅' = (2) - ∅ = (3)
• U' = (4) = ∅