About this topic
Before you begin
Read conditionals and quantifiers precisely, and form converses, contrapositives and negations.
Learning goals
- Identify the hypotheses, conclusions, quantifiers and connectives of a mathematical statement
- Form the converse, inverse and contrapositive and decide which are equivalent
- Negate statements with quantifiers and connectives
- Distinguish necessary, sufficient and equivalent conditions
Syllabus statements covered
- Include: Definition, Proposition and Theorem; Conditionals: if … then …, … if and only if …, Necessary, Sufficient; Quantifiers such as There exists (a unique) …, For all …; Logical connectives ‘and’, ‘or’, ‘not’, ‘implies’; Converse; Inverse; Contrapositive; Negation.
In this topic
Conditionals, quantifiers and negation
Read what a statement claims, form its converse, inverse and contrapositive, and negate quantified statements correctly.