UNI_BRIDGE · Proof & logic · PROOF.CONTRA

Contradiction and contrapositive

Intuition

Understand first, compress later.

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

Switch representations

Tree diagramP(R) = 0.6, P(B) = 0.4

R = red marbleB = blue marbleedge probability

Two draws with replacement: every edge carries the probability of that step. Along a path you multiply (0.6 · 0.4 = 0.24), across the four paths you add — and the four leaves total 1, as they must.

Formal view

You can contradiction and contrapositive 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.