6120a Discrete Mathematics And Proof For Computer Science Fix ✪

6120a uses a precise set language. Programming intuition fails here because 2,2,3 is still 2,3 in math—sets have no duplicates.

Memorize this equivalence: (P → Q) ≡ (¬P ∨ Q). If you ever get confused by an implication, rewrite it as an OR. 6120a uses a precise set language

Example Fix:

When to use: You need to prove ∀x (A(x) → B(x)). Template: Common Fix: Never say "Assume P is true

Common Fix: Never say "Assume P is true. Then obviously Q." Show the algebraic/relational steps. 3 is still 2

| Concept | Fixed Notation | |-----------------------|------------------------------| | Natural numbers | ℕ = 0, 1, 2, … (specify if 1‑based) | | Empty set | ∅ | | Set difference | A \ B (not A − B) | | Complement (relative) | ∁_U A or ~A when U is clear | | Power set | 𝒫(A) | | Tuple | (a₁, a₂, …, aₙ) | | Relation composition | R ∘ S | | Floor/ceiling | ⌊x⌋, ⌈x⌉ | | Graph G | (V, E) | | Binomial coefficient | (\binomnk) (not C(n,k) unless specified) | | Implication | P → Q (not P ⇒ Q) for object language | | Logical equivalence | P ≡ Q |

All proof exercises must use this fixed notation.