Set

An unordered collection of objects, duplicate doesn’t matter. The order in which you describe the elements doesn’t matter either.

{1, 2, 3} = {3, 2, 2, 1, 3}

Color = {Yellow, Blue}

Yellow = {Red, Green}

Here, Yellow ∈ Color but Red ∉ Color

When 𝑋 and 𝑌 are two sets, we say that 𝑋⊂𝑌 if every element of 𝑋 is contained in 𝑌.

∅ vs 0

Say, B = {x| x = your bank balance}

B = {} means you don’t have an account in any bank

B = {0} means you have an account with a 0 balance

∅ ⊆ any set, X

X ⊆ X

A ⊆ B iff A ∪ B = B

A ⊆ B iff A ∩ B = A

P( {} ) = { {} }

Click here for the empty set