Set intersection

In set theory, the intersection of two sets is a set containing all elements that are members of both sets. The symbol, ∩, is used to indicate a set intersection.

For example, suppose that Γ and Δ are sets of formulae, as defined as:

  • Γ = { α, β, φ }
  • Δ = { β, φ, ρ, ω }

The intersection Γ ∩ Δ is therefore the following set:

  • Γ ∩ Δ = { β, φ }

The intersection of two sets can be defined as follows:

  • Γ ∩ Δ = {x| x∈Γ ∧ x∈Δ}

Which means, for any x that is an element of Γ ∩ Δ, x is an element of Γ, and x is a member of Δ.