Maths WorkshopMaths problems with full solutions

Sets and maps

21 problems · Set operations, power sets, injections, surjections and bijections.

Search problems Level

Ex.183De Morgan's law for sets

Ex.186Injective or surjective?

#maps #bijection

Ex.277Basic set operations

#sets #union #intersection #complement

Ex.278The empty set

#empty set #uniqueness #axioms

Ex.279Subset relations

#subset #inclusion #definition

Ex.286Cartesian product with seven elements

#Cartesian product #cardinality #impossible

Ex.572Cardinality of finite sets

#cardinality #finite sets #inclusion-exclusion

Ex.573Cartesian product

#Cartesian product #ordered pair #cardinality

Ex.574Complement laws

#complement #De Morgan #laws

Ex.575Distributive laws for sets

#distributivity #union #intersection

Ex.576The power set

#power set #subsets #cardinality

Ex.577Relations and their graphs

#relation #binary relation #graph

Ex.578Symmetric difference

#symmetric difference #XOR #sets

Ex.626Inclusion and complement

#inclusion #complement #direct proof #contradiction

Ex.627Inclusion and union with the complement

#inclusion #complement #equivalence

Ex.628Cardinality of the power set

#power set #cardinality #induction

Ex.1176Arbitrary unions and intersections

#arbitrary union #arbitrary intersection #family

Ex.1177Equivalence classes and partitions

#equivalence class #partition #quotient

Ex.1178Equivalence relations

#equivalence relation #reflexive #symmetric #transitive

Ex.1179Partial orders

#partial order #poset #relation

Ex.1882Russell's paradox

#Russell paradox #set theory #self-reference