Answer Happy

Part 4. Symbolization in Modern Quantificational Logic. For each of the following sentences, the meanings of the predicate letters have been stated, and there is exactly one correct listed answer for each sentence. Write the number of the correct symbolization in the blank on the right. Do not include the parentheses in your answer, just write the number. (For convenience, all the symbolic sentences here have been stated informally without writing the outer scoping parentheses for the quantifiers as we did in class and in the exercises.) This part is worth 10 points and covers two pages of 5 points each.
6. Everything is a goat or not a goat. G - is a goat (1) (wx) Gx V (vx) -GX (2) (vx) GXV (ax) -GX (3) (ax) GX V-GX (4) (vx) GX V-GX 7 No goats are hungry. G = is a goat, Huis hungry (1) (vx) Gx & -HX (2) (vx) GX-HX (3) (vx) -GxHx (4) -(vx) Gx x 8. Something is hungry, and something is not polite. His hungry, P = is polite (1) (9x) Hx & -PX (2) (ax) Hx & (ax) -PX (3) (vx) Hx &-Px (4) (ax) Hx & -(x) PX 9. Some hungry goats are polite. H = is hungry. G = is a goat, P = is polite (1) (Ex) (Hx & Gx) Px (2) (Ex) (HxGx) & Px (3) (3x) (Hx & Gx) & Px (4) (Ex) (HxGx) > PX 10. Every hungry goat is polite. H = is hungry, G = is a goat, P = is polite (1) (vx) (Hx & Gx) > PX (2) (vx) (HX & Gx) & PX (3) (vx) (HxGx) PX (4) (vx) (Hx > GX) & PX