Question

Translate the following sentences using a notation using terms, predicates, qualifiers, and logical connectives.

Use the letters indicated for predicates and proper nouns.

1. All seniors are dignified. (Sx, Dx).

2. Some juniors are pretty. (Jx, Px)

3. No freshman are dignified. (Fx)

4. Some seniors are both pretty and dignified.

5. Every freshman dates some junior (Dxy)

6. Betty is pretty but not dignified(b)

7. Anyone who likes Greek is either a senior or a junior (Gx)

8. Elizebeth does not date any freshman ( e, Dxy)

Answer 1

KEY SYMBOLS
-------------
~ = negation
& = conjunction
--> = conditional implication
E = existential quantifier
A = universal quantifier

1. All seniors are dignified. (Sx, Dx).
Sx is seniors
Dx : senior is dignified
Ax[S(x) -> L(x)]

2. Some juniors are pretty. (Jx, Px)
J(x) is juniors
P(x) is junior is pretty
Ex[J(x)->P(x)]

3. No freshman are dignified. (Fx)
F(x) is freshman
D(x) is Fresher is dignified
~Ax[F(x) -> D(x)]

4. Some seniors are both pretty and dignified.
Ax[F(x) -> (P(x) & D(x))]

5. Every freshman dates some junior (Dxy)
Ex[F(x)->J(x)]

6. Betty is pretty but not dignified(b)
Ax[B(x)->P(x) && ~D(x)]

7. Anyone who likes Greek is either a senior or a junior (Gx)
P(x) : person
Senior: S(x)
Junior : J(x)
Greek: G(x)
  
Ax[P(x) -> G(x)?S(x):J(x)]

8. Elizebeth does not date any freshman ( e, Dxy)
~Ex[e(x)->D(x)]