Using the syntax playground construct the following L3 formulas.
P10. ∀x(Fx ∧ Gx)
P11. ∀x(Fx→(¬Gx → Hx))
P12. (¬∃xFx → ∀xFx)
P13. ¬∃y(Gy ∧ Hy)
P15. ∀x(Fx → ¬Hx) → ∃x(Jx ∧ Gx)
P16. (∀y∃x(Fy ∧ Gx) → ∃x(Gx ∧ Fx))
Construct L3 symbolisations for each of the following sentences.
S12. Everything is blue.
S13. Something is round.
S14. All sweets are good.
S15. Some sweets are good.
S16. Some sweets aren't good.
S17. Something is round and something is square, but it is not the case that something is a round square.
Using ∃LOGIC construct annotated derivations showing that the following arguments are valid.
3:0 Fa ∴ Fa ∨ Ga
3:1 ∀xFx ∴ Fa