What does this Discrete Mathematics cheat sheet cover?

It has 10 sections: Logic, Equivalences, Predicates, Proofs, Sets, Functions, Counting, Recurrences, Graphs and Modular. Together they cover the topics a typical Discrete Mathematics exam tests, including propositional logic and truth tables, logical equivalences, predicates and quantifiers and proof techniques: direct, contrapositive, contradiction, induction.

Is the discrete math cheat sheet free?

The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.

Can I bring this Discrete Mathematics cheat sheet to my exam?

Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.

The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it corrected 3 statements before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.

Can I make a Discrete Mathematics sheet from my own notes?

Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

MathDiscrete Mathematics

Discrete Math Cheat Sheet — 1-page PDF

Logic, proofs, sets, functions, counting, recurrences, graphs, modular arithmetic. The whole course on one dense, printable page for your midterm or final, with every formula typeset and worked examples where they help.

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For a specific exam: Discrete Mathematics Final exam study sheet.

1 pageUS Letter
10 sections10 topics
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Preview of the one-page Discrete Mathematics cheat sheet: Logic, proofs, sets, functions, counting, recurrences, graphs, modular arithmetic — the whole course, one page

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What’s on it

The topics a typical Discrete Mathematics exam tests, all on the one page.

Propositional logic and truth tables
Logical equivalences
Predicates and quantifiers
Proof techniques: direct, contrapositive, contradiction, induction
Sets and set identities
Functions and relations
Counting principles, pigeonhole
Recurrence relations
Graph basics, trees
Modular arithmetic

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The free part of the sheet, section by section. Unlock the full sheet to read the rest, edit any block, and print it or save it as a PDF.

01Logic

Proposition: Statement with truth value $T$ or $F$ only.

$p$	$q$	$p \land q$	$p \lor q$	$p \to q$	$p \leftrightarrow q$
$T$	$T$	$T$	$T$	$T$	$T$
$T$	$F$	$F$	$T$	$F$	$F$
$F$	$T$	$F$	$T$	$T$	$F$
$F$	$F$	$F$	$F$	$T$	$T$

Negation

\neg (p \land q) \equiv \neg p \lor \neg q, \neg (p \lor q) \equiv \neg p \land \neg q

De Morgan

Implication

p \to q \equiv \neg p \lor q \equiv \neg q \to \neg p

False only when $p = T, q = F$

Biconditional

p \leftrightarrow q \equiv (p \to q) \land (q \to p) \equiv (p \land q) \lor (\neg p \land \neg q)

Same truth values

Taut/Contrad

tautology $: T$ always $;$ contradiction $: F$ always $;$ contingency $:$ sometimes T/F

02Predicates

Existential

\exists x P (x)

At least one $x$ makes $P (x)$ true

Negate quantifiers

\neg\forall x P (x) \equiv \exists x \neg P (x), \neg\exists x P (x) \equiv \forall x \neg P (x)

Order matters

\forall x \exists y P (x, y) \neq \equiv \exists y \forall x P (x, y)

switching quantifiers changes meaning

Watch out:Negate by flipping quantifiers and negating the predicate; do not just insert a $\neg$ in front of the whole formula.

03Proofs

Direct: assume hypotheses; derive conclusion.
Contrapositive: prove $\neg q \to \neg p$ instead of $p \to q$ .
Contradiction: assume negation of target; derive contradiction.
Cases: split into exhaustive cases; prove each.
Induction: base case + inductive step.

Contrapositive

p \to q \equiv \neg q \to \neg p

use when $q$ easier to negate

04Sets

Cardinality

∣ A \cup B ∣ = ∣ A ∣ + ∣ B ∣ - ∣ A \cap B ∣

finite sets

Watch out:Always specify the universe for complements $A^{c}$ ; otherwise $A^{c}$ is ambiguous.

05Functions

Function: $f : A \to B$ assigns each $a \in A$ exactly one $f (a) \in B$ . Domain $A$ , codomain $B$ , range $f (A)$ .
Injective: $f (a_{1}) = f (a_{2}) \Rightarrow a_{1} = a_{2}$ .
Surjective: $\forall b \in B \exists a \in A$ such that $f (a) = b$ .
Bijective: Injective + surjective; has inverse $f^{- 1} : B \to A$ .

Composition

(g \circ f) (x) = g (f (x))

defined when codomain of $f$ fits domain of $g$

Inverse test

f^{- 1} \circ f = id_{A}, f \circ f^{- 1} = id_{B}

iff $f$ bijective

Property	Test
Injective	$f (a_{1}) = f (a_{2}) \Rightarrow a_{1} = a_{2}$
Surjective	every $b \in B$ equals $f (a)$ for some $a \in A$
Bijective	injective and surjective
Inverse	exists iff bijective

06Recurrences

Characteristic

r^{n} = c_{1} r^{n - 1} + c_{2} r^{n - 2} \Rightarrow r^{2} - c_{1} r - c_{2} = 0

solve for roots $r$

Ex.Solve $a_{n} = 2 a_{n - 1}$ , $a_{1} = 3$ .

Geometric: $a_{n} = 3 \cdot 2^{n - 1}$ .

Watch out:Recurrences need enough initial conditions to determine a unique sequence.

07Graphs

Graph: $G = (V, E)$ with vertices $V$ and edges $E$ . Simple graph: no loops or multiple edges.
Degree: $de g (v)$ = number of incident edges; loop counts twice.

Handshaking

\sum_{v \in V} de g (v) = 2∣ E ∣

Tree

tree $⟺$ connected and acyclic

Tree edges

∣ E ∣ = ∣ V ∣ - 1

for any tree

Connected

every pair of vertices joined by a path

Cheat sheet locked

Also on the full Discrete Mathematics sheet

9 more sections, with every definition, formula and worked example. Unlimited unlocks every full sheet in the library to edit, print or save as a PDF, and makes unlimited sheets from your own notes.

Logic

Equivalences

Idempotent
Identity/Domination
Commutative
Associative
Distributive
Absorption
Double negation
Useful rewrite

Predicates

Predicate
Universe
Universal

Proofs

Induction
Strong induction

Sets

Set ops
Set laws
De Morgan
Difference
Distributive
Subset

Counting

Add rule
Product rule
Permutation
Combination
Binomial
Pigeonhole

Recurrences

Recurrence relation
Arithmetic
Geometric
Linear homogeneous

Graphs

Modular

Congruence
Add/mult
Powers
Reduction
Inverse

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FAQ

Questions

About the Discrete Mathematics sheet and making your own.

What does this Discrete Mathematics cheat sheet cover?: It has 10 sections: Logic, Equivalences, Predicates, Proofs, Sets, Functions, Counting, Recurrences, Graphs and Modular. Together they cover the topics a typical Discrete Mathematics exam tests, including propositional logic and truth tables, logical equivalences, predicates and quantifiers and proof techniques: direct, contrapositive, contradiction, induction.
Is the discrete math cheat sheet free?: The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.
Can I bring this Discrete Mathematics cheat sheet to my exam?: Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.
How accurate is it?: The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it corrected 3 statements before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.
Can I make a Discrete Mathematics sheet from my own notes?: Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

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