Indicate which of the following are formulas of PL, and which of those are sentences of PL.

1. Indicate which of the following are formulas of PL, and which of those are sentences of PL. For each formula, underline the main logical operator and indicate whether the formula is atomic, truth-functionally compound, or quantifed. For those that are not formulas, explain why not, and for those that are formulas but not sentences, explain why they are not sentences. a. ~ ~ ~ (Ay)Fya b. (Az)(Faz > Gz) c. (Ex)Fxa > (Ey)Gay d. (Az)(Fza > Gwy) e. ~ (Ea)Fa

Symbolize English sentences a–d in PL, using the following symbolization key

2. Symbolize English sentences a–d in PL, using the following symbolization key: UD: living things Nx: x is a nut-eater Bx: x is a black squirrel Gx: x is a gray squirrel Rx: x is a red squirrel a. All gray squirrels are nut-eaters. b. No gray squirrels are nut-eaters. c. Some gray squirrels are nut-eaters. d. Some gray squirrels are not nut-eaters.

Indicate which of the listed expressions are substitution instances

3. Indicate which of the listed expressions are substitution instances of '(Ax)(Ey)(Bxy > Byx)'. a. Bab > Bba b. (Ey)(Bay > Bya) c. (Ey)Bay > Bya d. (Ey)(Bcy > Byc)

Symbolize the following sentences, using the symbolization key given.

4. Symbolize the following sentences, using the symbolization key given. UD: Everything Px: x is a person Tx: x is a time Fxyz: x fools y at z a. No one can fool all of the people all of the time. b. Someone is never fooled.

Determine the truth-values of a–c on the following interpretation.

5. Determine the truth-values of a–c on the following interpretation. UD: Set of U.S. cities Bxyz: x is between y and z n: New York City c: Chicago s: San Francisco a. Bnsc v Bsnc b. (Ax)Bxcs > (Ex) ~ Bxcs c. (Ax)(~ Bxsc = Bscn)