Discrete & Logic
4 concepts
n(A∪B) = n(A) + n(B) − n(A∩B)Sets and Venn Diagrams
The size of the union is the two sets' sizes added, then the overlap (the intersection) subtracted exactly once.
(p → q) ≡ (~q → ~p)Propositions: True or False
A proposition is a sentence you can clearly judge true or false. A conditional like 'if p then q' always shares the same truth value as its contrapositive.
G = (V, E), Σ(v∈V) deg(v) = 2|E|Graph Theory
A graph is a collection of dots (vertices) and lines (edges) joining them. It records only what is connected to what, throwing away position, shape, and distance. It's a map of relationships stripped to the skeleton.
[ P(1) ∧ ( P(k) ⟹ P(k+1) ) ] ⟹ ∀n ≥ 1, P(n)Mathematical Induction
Mathematical induction proves statements true 'for every natural number n'. (1) Show it holds at n=1 (the base), and (2) show that if it holds at n=k it must hold at n=k+1 (the step); like dominoes, they all fall.
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