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.

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:

Compute a truth table for a Boolean function:

Compute a logic circuit for a Boolean function:

Convert a Boolean expression to disjunctive normal form:

More examples
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:

Simplify an expression involving cardinals:

More examples
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:

Test whether a given equation of sets is true:

More examples