# Logic

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1. Give a proof of the following:

(∀F)( (P)( [ιxGx][Px] ⊃ F(P) ) ⊃ F(G))

(∃F)( (P)( F(P) ≡ [ιxGx][Px])

Therefore, E!(ιxGx)

2. Prove the following:

[ιxMx][Thales believed that Bx]

[ιxMx][ιyEy][x=y]

Therefore, [ιxEx][Thales believed that Bx]

3. Prove the following:

Kepler Believed that (9 > 7)

(∃x)( (z)(Pz ≡ z=x) • x = 9)

Therefore, (∃x)( (z)(Pz ≡ z=x) • Kepler believed that (x>7))

a) The fastest man on Earth is not superman. Mx: x is a man; Fxy: x is faster than y; Sx: x lives on Earth but was born on Krypton. (Express it first with scope markers and then translate. There are two scopes.)

b) Pegasus is not equal to Pegasus. Px: x is winged and a horse. (Express first with scope markers and then translate. There are two scopes.)

c) Oedipus believed that Jocasta was not his mother. (Hint: Oedipus is famous for marrying his mother Jocasta, not knowing she is his mother. Give a primary scope occurrence for the description of Jocasta as “the mother of Oedipus.” Pxy: x gave birth to y; Ox: x is most famous topic of psychoanalysis. “Jocasta” is replaced by “the mother of Oedipus,” which is (ιx)[ιyOy][Pxy].