UNI_BRIDGE · Proof & logic · PROOF.SETS

Sets, functions and relations

Intuition

Understand first, compress later.

A proof is an unbroken chain of reasoning from definitions, assumptions and established results.

Switch representations

Venn diagram|Ω| = 22

universe ΩsetsA ∩ B

The two circles cut the universe into four regions: only A (7), A ∩ B (5), only B (4), and outside both (6). Adding the sizes of A and B counts the shared region twice — which is why it is subtracted once.

Formal view

You can sets, functions and relations when you can recognise the underlying objects, select valid rules and check each step for equivalence or logical implication.

Why does it work?

This skill sits on a prerequisite network. If a step is unstable, repair the missing prerequisite instead of merely doing more items of the same type.