"Greg dreams of both Ferraris and Porsches."

Question

What is the best propositional logic translation for the following? 

"Notre Dame raises tuition if Purdue does."

a. (P ⊃ N)

b. (N ⊃

c. (N ⊃ P)

d.( ⊃ )

"Prozac relieves depression and Allegra combats allergies, or Crestor lowers cholesterol.

a. ((P • A) v C)

b. ((P v A) v C)

c. ((P • A) • C)

d. ((P v A) • C)

"Neither John nor Lisa knows the answer."  

a. ~(J v L)

b. ~(J • L)

c. (~J v ~L)

d. (~ J L)

"Either Salvador Dali or Pablo Picasso ignored perspective, but it is not the case that both of them did." 

a. ((S v P) • N)

b. ((S • P) • ~(S • P))

c. ((S v P) • ~(S • P))

d. ((S v P) v ~(S • P))

"Greg dreams of both Ferraris and Porsches."

a. (F ⊃ P)

b. (F v P)

c. (F • P)

d. GDFP

Answer 1

#1 is A : (P ⊃ N)

#2 is also A: (P • A) v C)

#3 is noteworthy. The answer is again A: ~(J v L)

John does not know the answer AND Lisa does not know the answer,

so ~J and ~L = ~( J or L) by DeMorgan's

#4 is C: ((S v P) • ~(S • P)), and I will prove it via truth table

#5 is also C : (F • P)

Truth table to show that the answer to #4 is the same as S xor P

S | P | S or P | S and P | ~(S and P) | answer to #4 | S xor P

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T T T T F F F

T F T F T T T

F T T F T T T

F F F F T F F

Xor is the EXCLUSIVE OR and has the truth table

T xor T = F

F xor T = T

T xor F =T

F xor F = F

it works like the regular OR except if both are true, the result is FALSE.

This is exactly the situation in problem #4