Translating the ordinary language statements into predicate logic symbolic form.

Translation Questions 1 - 10: (5 marks each 50 marks total) Translate the following ordinary language statements into predicate logic symbolic form. You can use the predicate letters that are provided. Questions #7 - #10 are more advanced, please note the extra instructions for them.

1. Ginger is a spice (G, S)
2. Jimmy Carter was not an academy award winner. (A)
3. Cell phones are not universally admired products. (C, U)
4. Some SUVs are not environmentally friendly vehicles. (B, C)
5. All whole numbers are either even or odd. (W, E, O)
6. Everything that is alive is mortal. (A, M)

Questions #7 - #10 are translations involving relational predicates, overlapping quantifiers, and identity. You can use the predicate letters provided.

1. Something destroyed everything. (Dxy: x destroyed y)
2. Everyone is a child of someone. (Cxy: x is a child of y)
3. Anyone who reads Kant reads Hume. (Rxy: x reads y, k: Kant, h: Hume)
4. Stan Lee invented Marvel Comics. (Ixm: x invented Marvel Comics; s: Stan Lee)

Proof of Validity Questions 11-14: (10 marks each) The following 4 arguments are valid. Provide a proof of validity for each argument. You can use the 18 rules of inference, CP, IP, the rules for introducing and removing quantifiers and the Change of Quantifier rules. Questions #13 #14 are more challenging, they involve relational predicates, overlapping quantifiers, and identity.

11.

1. ($x) Fx É ($x) (Gx • Hx)
2. ($x) Hx É (x) Jx \ (x) (Fx É Jx)
3. (x) (Fx É Hx)
4. (x) (Fx É Gx) /\ (x) [ Fx É (Gx · Hx)]
5. ($x) [Lx · (y) (My É Pxy)] /\ ($x) [Lx · (Mb É Pxb)]

14.

1. ~ Lb
2. (x) [ Hx É ( Lx · x = b)] /\ ~ Ha

Proving Invalidity Question 15: (10 marks) The following argument is invalid. Show it to be invalid using the finite universe method.

1. ($x) (Gx · Lx)
2. ($x) (Gx · Hx) /\ (x) (Lx É Hx)

Sample Solution