Relationships between sets
Check inclusion and operation laws using conditions on elements.
Meaning
Inclusion and operation laws let us rewrite complex conditions in equivalent forms. De Morgan's laws connect complements of unions and intersections.
Example
People who play neither soccer nor basketball form the intersection of those who do not play soccer and those who do not play basketball. This says that the complement of a union is the intersection of the complements. “Not both” and “neither” mean different things. Check which whole condition is being negated.
Practice for this concept
Scope and references
Topics
Inclusion, laws of set operations, De Morgan's laws
Learning goal
Check inclusion and operation laws using conditions on elements.
Helpful background
Connect set operations with and, or, and negation.
Set relationships
These choice exercises use specified finite sets, conditions, or proof steps. They do not establish constructing new counterexamples or proofs, or mastery of the whole logic area.