Set Comprehensions
Set Comprehension
A way to describe a set using a rule or condition.
Example: {x | x > 5}
Logical Formula (Φ)
A condition that decides whether an element belongs to a set.
Example: x is even
Restricted Set Comprehension
Creates a set using elements from another set that satisfy a condition.
Example: {x ∈ N | x < 10}
Pair Set Comprehension
Creates sets using ordered pairs that satisfy a condition.
Example: {(x, y) | x + y = 5}
Even Natural Numbers
Natural numbers divisible by 2.
Example: E = {y ∈ N | y = 2 × z}
Odd Natural Numbers
Natural numbers that are one more than an even number.
Example: O = {y ∈ N | y = z + 1}