Answer by ryang for What is the weird correspondance between subset ⊂ and implication ⇒?

using (p ⇒ q) ≡ (¬p∨q) yielded a weird Venn diagram

Okay, this is the Venn diagram (here, white space signifies that no element is contained there) that you are referring to:

This diagram says: If it belongs to set $A,$ then it also belongs to set $B.$

In this answer, I displayed the Euler diagram of $$\forall x \,\Big(A(x)\to B(x)\Big)$$ as this:

For your example, $A$ and $B$ denote the set of cats and cunning objects, respectively, so that “Every cat is cunning.”

Observe that these two diagrams correspond to each other.