Unformatted text preview: (.q) r] using 12 again. (g) .(p V q) V [(.p) /\ q] {=} [(.p) /\ (.q)] V [(.p) /\ q] (DeMorgan) {=} (.p) /\ [(.q) V q] (distributivity) {=} (.p) VI{=} 'P 6. [(p/\(.q))q] {=} [(.(p/\(.q)))Vq] {=} [((.p)Vq)Vq] {=} [(.p)Vq]. [(P/\(.q))(.p)] {=} [(.(p/\(.q))) V (.p)] {=} [(.p)VqV('p)] {=} [(.p)Vq]. So these are both logically equivalent to (.p) V q. 7. (a) We must show that A V e and 13 V e have the same truth tables, given that A and 13 have the same truth tables. This requires four rows of a truth table. A 13 e AVe 13ve T T T T T T T F T T F F T T T F F F F F The last two columns establish our claim. (b) We must show that A /\ e and 13 /\ e have the same truth tables, given that A and 13 have the same truth tables. This requires four rows of a truth table. A 13 e A /\ e 13/\e T T T T T T T F T T F F T F F F F F F F The last two columns establish our claim....
View
Full Document
 Summer '10
 any
 Graph Theory

Click to edit the document details