quantifications

Summary

Universal statements

• true iff is true for every in
• false iff is false for one or more in
• disprove by counterexample

Existential statements

• true iff is true for one or more in
• • false iff is false for every in
• prove by example

Negation

• if is false for all values of , then there exists one or more where is false
• if there does not exists one or more where is true, then is false for all values of

Concept

Universal quantification(for all) ->
Existential quantification(there exists) ->

Domain ->
Predicate ->

Sensitive to domain, which may be a number set

Composed quantified statements

Expanding quantification

Universal conditional statements

Application

Universal statement

• prove for all values

• disprove by counterexample

Existential statement

• prove by example

• disprove for all values

Negation of composite statements