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ProblemsClear skill: Logic Proof Build a practice set

ProblemCourse & topicStatus

DM:9919001Let p, q, and r be propositions.

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

—

DM:9919002Let p, q, and r be propositions.

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

—

DM:9919003Mathematical problem title

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

—

DM:9919004Determine, with a truth table, whether the argument…

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

—

DM:9919005Express the English sentence “A student passes the course if and only if the student attends every lecture and…

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

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DM:9919006Let P(x) denote “x is prime” and E(x) denote “x is even”, where the domain of discourse is the set of positive…

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

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DM:9919007Let the domain of discourse be the set of all real numbers.

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

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DM:9919008Let the domain be the set of all people, and let L(x,y) mean “x likes y”.

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

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DM:9919009Let the domain of discourse be the integers.

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

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DM:9919010Consider the open sentences P(x,y): “x divides y” and Q(x): “x is odd”, with domain the set of integers.

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

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DM:9919011Mathematical problem title

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

—

DM:9919012Mathematical problem title

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

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DM:9919013Let a, b, and c be integers.

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

—

DM:9919014Mathematical problem title

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

—

DM:9919015Mathematical problem title

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

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DM:9919016Mathematical problem title

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

—

DM:9919017Mathematical problem title

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

—

DM:9919018Let P(n) be the statement “n²+n is even”.

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

—

DM:9919019Mathematical problem title

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

—

DM:9919020Mathematical problem title

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

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DM:9919021Mathematical problem title

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

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DM:9919022Mathematical problem title

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

—

DM:9919023Mathematical problem title

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

—

DM:9919024Let A, B, and C be sets.

Logic ProofDiscrete Mathematics Problem Solving

Propositional and predicate logic with proof methodsDiscrete Mathematics · Calculation

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Showing 24 of 43 matching problems.

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Negate the compound proposition

(\neg p \lor q) \land (r \to \neg q)

and simplify the result so that negation…

Prove that for every integer n, if

n^2

is even then n is even, by proving the contrapositive.

Prove that there is no integer n such that

n^2\equiv

2\pmod{4}

.

Prove that

\sqrt{2}

is irrational.

Prove by contradiction that if A and B are sets with

A\cap

B=\emptyset

and

A\cup

B=A, then

B=\emptyset

.

Prove that for every positive integer

n

,

1+3+5+\cdots+(2n-1)=n^2

by mathematical induction.

Prove by induction on

n

that for every integer

n\ge 0

and every real number

x\neq 1

…

(Honors) Prove that for every integer

n\ge 1

,

\sum_{k=1}^{n} k\cdot 2^k=(n-1)\cdot 2^{n+1}+2

by induction.

Let

A=\{1,2,3,4\}

and

B=\{3,4,5,6\}

.

Let

U=\{1,2,3,4,5,6,7,8\}

be the universe,

A=\{1,2,3,4\}

, and

B=\{3,4,5,6\}

.

Using only the definitions of union, intersection, and complement (element-chasing), prove that for all sets

A

…

Prove that for all sets

A

and

B

,

A\setminus B=A\cap B^c

, where complements are taken relative to a fixed…