2. An ugly rumor is spreading around the office about you! You want to figure out which person started
it. We suppose you know it was a single person who started it, and it has to be one of your friends:
Dakota, Emory, Flynn, and Grady. You have interviewed Dakota, Emory, Flynn, and Grady and they
have made statements, $S_D$, $S_E$, $S_F$ and $S_G$ respectively. The statements are as follows
$S_D$: "Emory or Flynn started it."
$S_E$: "Flynn or Grady started it."
$S_F$: "Dakota didn't start it."
$S_G$: "Dakota or Emory started it."
[8 points] (Most relevant reading: BoP 2.6-2.9)
1
(a) Let the logic variables D, E, F, and G correspond to whether Dakota, Emory, Flynn, and Grady
are the origin of the rumor. Using these variables, write logic expressions for each of the four
statements made. [2 points]
(b) Use a truth table to evaluate the value of all four statements for every possible combination of
truth values for D, E, F,and G where exactly one of these is true (ie, FFFT, FFTF, ...). [2
points]
(c) For which of the combinations of truth values that you analyzed in part b does only one of the
four statements evaluate as false? [2 points]
(d) Suppose that only the person who started the rumor would make a false statement to you. Who
started the rumor? [2 points]
