Set Theory Symbols

Question 1

What does the symbol ∈ mean?

Answer 1

• Name: Element of
• Purpose: Checks if an element is in a set
• Example: $3 \in {1, 2, 3, 4}$

None

Question 2

What does the symbol ∉ mean?

Answer 2

• Name: Not an element of
• Purpose: Shows an element is not in the set
• Example: $5 \notin {1, 2, 3}$

None

Question 3

What does the symbol ⊆ mean?

Answer 3

• Name: Subset
• Purpose: Every element in A is also in B
• Example: ${1, 2} \subseteq {1, 2, 3}$

None

Question 4

What does the symbol ⊂ mean?

Answer 4

• Name: Proper Subset
• Purpose: A is a subset of B but not equal to B
• Example: ${1, 2} \subset {1, 2, 3}$

None

Question 5

What does the symbol ⊄ mean?

Answer 5

• Name: Not a subset
• Purpose: A is not a subset of B
• Example: ${4} \not\subseteq {1, 2, 3}$

None

Question 6

What does the symbol ∪ mean?

Answer 6

• Name: Union
• Purpose: Combines elements from both sets (no duplicates)
• Example: ${1, 2} \cup {2, 3} = {1, 2, 3}$

None

Question 7

What does the symbol ∩ mean?

Answer 7

• Name: Intersection
• Purpose: Finds elements common to both sets
• Example: ${1, 2} \cap {2, 3} = {2}$

None

Question 8

What does the symbol − mean in sets?

Answer 8

• Name: Set Difference
• Purpose: Elements in A but not in B
• Example: ${1, 2, 3} - {2, 3} = {1}$

None

Question 9

What does P(A) mean?

Answer 9

• Name: Power Set
• Purpose: All subsets of set A
• Example: $P({1, 2}) = {\varnothing, {1}, {2}, {1,2}}$

None

Question 10

What does the symbol ∅ mean?

Answer 10

• Name: Empty set
• Purpose: A set with no elements
• Example: $\varnothing = {}$

None

Question 11

Symbol:** P(A)

Answer 11

• Name: Power Set
• Purpose: The set of all possible subsets of set A
• Example:
  If $A = {1, 2}$, then:$$
  P(A) = {\emptyset,\ {1},\ {2},\ {1,2}}
  $$

Question 12

12. Symbol: { x : condition }

Answer 12

• Name: Set-builder notation
• Purpose: Defines a set by a rule instead of listing elements
• Example:$$
  {x : x \text{ is even and } x < 10} = {2, 4, 6, 8}
  $$

Question 13

13. Symbol: : or |

Answer 13

• Name: Such that
• Purpose: Introduces the condition in set-builder notation
• Example:$$
  {x \in \mathbb{Z} : x > 0} = \text{All positive integers}
  $$