Chapter 1 - Section 1.3 - Propositional Equivalences - Exercises - Page 34: 7

a) Jan is not rich or not happy b) Carlos will not bicycle and not run tomorrow c) Mei does not walk and does not takes the bus to class. d) Ibrahim is not smart or not hard working

$\neg (p \lor q)$ = (($\neg p)\land(\neg q))$ $\neg (p \land q)$ = (($\neg p)\lor(\neg q))$ _______________________________________________________________________________ a) NOT [(Jan is rich ) and (happy)]= [NOT(Jan is rich) or NOT( happy)]= Jan is not rich or not happy b)NOT [(Carlos will bicycle) or (run tomorrow)]= [NOT(Carlos will bicycle) and NOT(run tomorrow)]= Carlos will not bicycle and not run tomorrow. We could also render this as "Carlos will neither bicycle nor run tomorrow". c) NOT [(Mei walks) or (takes the bus to class)]= [NOT (Mei walks) and NOT (takes the bus to class)]= Mei does not walk and does not takes the bus to class. We could also render this as "Mei neither walks nor takes the bus to class". d) NOT[( Ibrahim is smart) and (hard working)]= [NOT( Ibrahim is smart) and NOT(hard working)]= Ibrahim is not smart or not hard working.