Miscellaneous Examples

This closing set of examples does not introduce any new idea — instead, it draws together everything built up across the chapter: recognising statements, forming negations, breaking compound statements into their components, applying the rules for "And"/"Or", handling quantifiers, rewriting implications in their equivalent forms, taking a converse or contrapositive, and validating a claim by the direct, contrapositive, contradiction or counter-example method. Working through these combined problems is the best way to see …