a) [ιxMx][ιyFxy][ιzSz][Fxy • Sx • ¬Sy]
[∀x][Mx ⊃ [∀y][Fxy ⊃ [∀z][Sz ⊃ (Fxy • Sx • ¬Sy)]]
b) [ιxPx][ιyPy][¬(x=y)]
[∀x][Px ⊃ [∀y][Py ⊃ ¬(x=y)]]
c) [ιxOx][¬[ιyOy][Pxy]]
[∀x][Ox ⊃ ¬[ιyOy][Pxy]]
Even if you know only some of them please help!
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].
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