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Discrete Mathematics with Graph Theory (3rd Edition) 22

# Discrete Mathematics with Graph Theory (3rd Edition) 22 -...

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20 Solutions to Exercises p 0 pVO 8. The truth table shows that p y.. 0 <=> p: T F T F F F p -,p p V (-,p) 1 9. [BBJ The truth table shows that ( P Y (-,p» <===? 1: T F T T F T T T 12. [BBJ This is no longer true: Finally, neither law of absorption holds: p y.. (p/\q) is not logically equivalent to p andp/\ (p y.. q) is not logically equivalent to p. I ~ I ; I p; q I p V ~ /\ q) I I ~ I ; I p; q I p /\ ~ V q) I 9. (a) (p V q) /\ «-,p) V (-,q)) is notin disjunctive normal form because the terms are not joined by V. (b) [BBJ (p /\ q) V «-,p) /\ (-,q» is in disjunctive normal form. (c) [BBJ p V «-,p) /\ q) is notin disjunctive normal form: not all variables are included in the first term. (d) (p /\ q) V « -,p) /\ (-,q) /\.r) is not in disjunctive normal form: not all variables are included in the first term. . (e) (p /\ q /\ r) V « -,p) /\ (-,q) /\ (-,r)) is in disjunctive normal form. 10. (a) [BBJ This is already in disjunctive normal form! The definition permits just a single midterm.
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