Question

I posted these question before but the answers turned out wrong, please help.(Monadic predicate logic) The ones required are = ( tilde ~ for negation, dot • for conjuction, horseshoe ⊃ for material implication( the conditional ), vel ∨ for disjunction, triple bar ≡ for biconditional ) Please use these symbols.

translate the following English sentences into Predicate Logic: 1. All philosophers are scientists. (Px, Sx) 2. Some mathematicians are philosophers. (Mx, Px) 3. No chess players are video gamers. (Cx, Vx) 4. Some chess players are not poker players. (Cx, Px) 5. Not all books are interesting. (Bx, Ix) 6. Every computer is a machine. (Cx, Mx) 7. No computer is intelligent. (Cx, Ix) 8. Some programmers are intelligent. (Px, Ix) 9. Some programmers are not intelligent. (Px, Ix) 10. Most programmers are intelligent. (Px, Ix)

Part II translate the following English sentences into Predicate Logic using the key provided. Assume that the we are always talking about people, so it is never necessary to specify that something is a person (so we do not need the predicate Px: x is a person). b: Berkeley h: Hume Ax: x is an apriorist Cx: x is consistent Ex: x is an empiricist Ix: x is idealistic Rx: x is a rationalist Sx: x is skeptical Tx: x is a theist 1. Berkeley is skeptical, but he is not a theist. 2. Every theist is a rationalist. 3. There are no skeptical theists. 4. Some idealistic empiricists are theists. 5. Everyone is a theist unless someone is both skeptical and not an apriorist. 6. If some rationalist is also an empiricist, then every theist is consistent. 7. Hume is a theist only if Berkeley is an apriorist. 8. Berkeley and Hume are both empiricists, but neither of them is a theist. 9. Some apriorist is skeptical if, and only if, she is a consistent empiricist. 10. Every theist is consistent or some theist is not consistent.

Answer 1

Answer:
Solving the questions using 'Monodic Predicate logic'.
[Tilde ~ for Negation] [dot . for conjunction] [ horseshoe > for material implication(conditional)]
[vel v for disjunction] [ Triple bar = for biconditional]

ASSUMPTIONS for symbols
@ for All/EVERYONE    $ for some/something   * To use along with $

Part 1 {10 questions}
1. All philosophers are scientists Px, Sx              REQUIRED EXPRESSION[ @x(Px > Sx)]
2. Some mathematicians are philosophers. (Mx, Px)      REQUIRED EXPRESSION[ $x(Mx * Sx)]
3. No chess players are video gamers. (Cx, Vx)         REQUIRED EXPRESSION[ ~$x(Cx * Vx)]
4. Some chess players are not poker players. (Cx, Px) REQUIRED EXPRESSION[ $x(Cx * ~Px)]  
5. Not all books are interesting. (Bx, Ix)             REQUIRED EXPRESSION[ ~@x(Bx > Ix)]
6. Every computer is a machine. (Cx, Mx)               REQUIRED EXPRESSION[ @x(Cx > Mx)]
7. No computer is intelligent. (Cx, Ix)                REQUIRED EXPRESSION[ ~$x(Cx * Ix)]
8. Some programmers are intelligent. (Px, Ix)          REQUIRED EXPRESSION[ $x(Px * Ix)]
9. Some programmers are not intelligent. (Px, Ix)      REQUIRED EXPRESSION[ $x(Px * ~Ix)]
10. Most programmers are intelligent. (Px, Ix)         REQUIRED EXPRESSION[ $x(Px * Ix)]

Part 2 {10 questions}
Assume that the we are always talking about people, so it is never necessary to specify that something is a person (so we do not need the predicate Px: x is a person).
b: Berkeley h: Hume Ax: x is an apriorist Cx: x is consistent Ex: x is an empiricist Ix: x is idealistic Rx: x is a rationalist Sx: x is skeptical Tx: x is a theist
1. Berkeley is skeptical, but he is not a theist.                               REQUIRED EXPRESSION [Sh & ~Tb]
2. Every theist is a rationalist.                                               REQUIRED EXPRESSION [@x(Tx > Rx)]
3. There are no skeptical theists.                                              REQUIRED EXPRESSION [~@x(Sx & Tx)]
4. Some idealistic empiricists are theists.                                     REQUIRED EXPRESSION [$E(IE * TE)]
5. Everyone is a theist unless someone is both skeptical and not an apriorist.

REQUIRED EXPRESSION [@xTx --> $x(Sx & ~Ax)]
6. If some rationalist is also an empiricist, then every theist is consistent.

REQUIRED EXPRESSION [ $x(Rx * Ex) --> @x(Tx > Cx)]
7. Hume is a theist only if Berkeley is an apriorist.              

             REQUIRED EXPRESSION [ Ab --> Tb]                       ]
8. Berkeley and Hume are both empiricists, but neither of them is a theist.    

REQUIRED EXPRESSION [ E(b & h) --> ~T(b& h) ]
9. Some apriorist is skeptical if, and only if, she is a consistent empiricist. REQUIRED EXPRESSION

[ $x(Ax & Sx) --> [ Ex(h) ]
10. Every theist is consistent or some theist is not consistent.              

REQUIRED EXPRESSION [ @x(Tx → Cx) v $x(Tx & ~Cx) ]

Above are translations using predicate logic concepts. Thanks