using Catlab.Graphs, Catlab.Graphics
using Catlab.Theories, Catlab.CategoricalAlgebra

G = cycle_graph(Graph, 4) ⊕ path_graph(Graph, 2) ⊕ cycle_graph(Graph, 1)
add_edge!(G, 3, add_vertex!(G))

to_graphviz(G, node_labels=true, edge_labels=true)

(A = Subobject(G, V=1:4, E=[1,2,4])) |> to_graphviz

(B = Subobject(G, V=[2,3,4,7,8], E=[2,3,6,7])) |> to_graphviz

A ∨ B |> to_graphviz

A ∧ B |> to_graphviz

(A ⟹ B) |> to_graphviz

¬A |> to_graphviz

(C = Subobject(G, V=1:4)) |> to_graphviz

¬(¬C) |> to_graphviz

(A \ B) |> to_graphviz

~A |> to_graphviz

(A ∧ ~A) |> to_graphviz