Propositional Logic: Translation Practice

25 flashcards

Translation the following ordinary language sentence into propositional logic notation: This is not chocolate ice cream.

~ C

Translation the following ordinary language sentence into propositional logic notation: This is not chocolate ice cream, but it is delicious.

~ C • D

Translation the following ordinary language sentence into propositional logic notation: Unless you have time, you can't go to the movies.

T V ~ M Alternate, logically equivalent translation: ~ T ƒ ~ M

Translation the following ordinary language sentence into propositional logic notation: Either you go to the movies today or you go to the library.

M V L

Translation the following ordinary language sentence into propositional logic notation: If you can't go to the movies today, you go to the library.

~ M ƒ L

Translation the following ordinary language sentence into propositional logic notation: You can't both go to the movies and the library today.

~ (M • L) Alternate, logically equivalent translation: ~ M V ~ L

Translation the following ordinary language sentence into propositional logic notation: The wind blew the candle out and now I can't see clearly.

W • ~ S

Translation the following ordinary language sentence into propositional logic notation: Both our teams, baseball and football, are up for a national championship.

B • F

Translation the following ordinary language sentence into propositional logic notation: Neither pancakes nor waffles are available at this restaurant.

~ (P V W) Alternate, logically equivalent translation: ~ P • ~ W

Translation the following ordinary language sentence into propositional logic notation: It's cloudy today, but it doesn't look like it's going to rain.

C • ~ R

Translation the following ordinary language sentence into propositional logic notation: Not both Vimeo and YouTube are free platforms for businesses.

~ (V • Y)

Translation the following ordinary language sentence into propositional logic notation: Only if you have time do you go to the movies.

M ƒ T

Translation the following ordinary language sentence into propositional logic notation: If you're happy and you know it, you clap your hands.

(H • K) ƒ C

Translation the following ordinary language sentence into propositional logic notation: If you're happy, then, if you know it, you clap your hands.

H ƒ (K ƒ C)

Translation the following ordinary language sentence into propositional logic notation: If you have neither the time nor the inclination, you don't go to the movies.

~ (T V I) ~ M

Translation the following ordinary language sentence into propositional logic notation: You go to the library or the movies today, but you definitely eat pizza in either case.

(L V M) • P

Translation the following ordinary language sentence into propositional logic notation: You go to the library and eat pizza today, or you go to the movies and eat pizza today.

(L • P) V (M • P)

Translation the following ordinary language sentence into propositional logic notation: Earning an A in logic class guarantees you have satisfied your critical reasoning requirement.

L ƒ C

Translation the following ordinary language sentence into propositional logic notation: My cat deigns to say hello if, and only if, I have fed him tasty treats.

D a T

Translation the following ordinary language sentence into propositional logic notation: Feeding my cat tasty treats is both necessary and sufficient for him to deign to say hello.

D a T

Translation the following ordinary language sentence into propositional logic notation: You either see Tweedledee with Tweedledum, or you see neither of them.

(E v U) v ~ (E V U) Alternate, logically equivalent translation: E a U

Translation the following ordinary language sentence into propositional logic notation: You don't see Tweedledee without Tweedledum, and you don't see Tweedledum without Tweedledee.

There are a few logically equivalent options here: (~ E ƒ ~ U) • (~ U ƒ ~ E) (U ƒ E) • (E ƒ U) (E V ~ U) • (U V ~ E) E a U

Translation the following ordinary language sentence into propositional logic notation: If I don't have enough cash, then I can't both go to the movies and eat out.

~ C ƒ ~ (M • E) Alternate, logically equivalent translations: C V ~ (M • E) ~ C ƒ (~ M V ~ E)

Translation the following ordinary language sentence into propositional logic notation: I can go to the movies and eat out only if I have enough cash.

(M • E) ƒ C Alternate, logically equivalent translation: M ƒ (E ƒ C)

Translation the following ordinary language sentence into propositional logic notation: Unless I am mistaken, you're a wonderful person and you have great taste in clothes.

M V (W • G) Alternate, logically equivalent translation: (M V W) • (M V G)