Examples for

Logic & Set Theory

Symbolic logic and set theory are intertwined and lie at the foundations of mathematics. Use Wolfram|Alpha to visualize, compute and transform logical expressions or terms in Boolean logic or first-order logic. Wolfram|Alpha will also create tables and diagrams, perform set-theoretic operations and compute set theory predicates like equality and subset.

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Boolean Algebra

Compute truth tables, find normal forms and construct logic circuits for any Boolean expression of any number of Boolean variables.

Analyze a Boolean expression:

P && (Q || R)

Compute a truth table for a Boolean function:

truth table p xor q xor r xor s

Compute a logic circuit for a Boolean function:

logic circuit (p or ~q) and (r xor s)

Convert a Boolean expression to disjunctive normal form:

DNF (P || Q || R) && (~P || ~Q)

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Set Theory

Test for set membership, set equality and subset relations. Draw a Venn diagram for a moderate number of sets.

Generate a Venn diagram:

(A union B) intersect C

symmetric difference of S and T

Test whether a given equation of sets is true:

is (A union B)'=(A') intersect (B')

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Transfinite Numbers

Perform arithmetic operations and simplify expressions involving infinite cardinals. Test cardinal numbers for cardinal equality or explore cardinal inequality.

Get information about a transfinite cardinal:

aleph0

Simplify an expression involving cardinals:

5*aleph0^aleph0

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