Symbolic Logic - Translation
Translate the following statements into symbolic logic form using capital letters to represent each simple statement, and using the logical operators to construct the compound statements. The capital letters you are using for each simple statement are indicated by being in parentheses. You must define what each of the capital letter represents. Be careful to represent parts of compounds that need to be separated from the main logical connective of parentheses.
(Hint: Common mistakes include using a ⊃ for both the If and the Then when it should only be placed in the Then position. Also, negations come before the item/statement/compound they negate.)
For reference, the following symbols should be used:
~ = Not
& = And
v = Or
⊃ = If... Then
≡ = If and only if
Use the following examples as a guide.
Examples:
- (S)witzerland is not a violent country.
- Both (C)ats and (D)ogs make good pets, if they are (T)rained.
You should ONLY write your answers in a list.
- ~S: S = Switzerland is a violent country.
- T ⊃ (C&D): C = cats make good pets, D = dogs make good pets, T = pets are trained.
Problems
- New (Z)ealand does not have nuclear weapons.
- Both (P)oland and (I)reland outlaw abortion.
- (S)cotland declares independence if and only if (E)ngland reduces imports.
- (G)reenland's protecting its fishing rights, implies that (I)celand repays its debt.
- (H)ungary adopts political reforms and, either (R)omania freezes wages or (B)ulgaria broadens services.
- Both (P)akistan and (I)ndia do not take political prisoners.
- Neither (S)weden nor (N)orway reduces deficit spending.
- If (C)anada's creating jobs implies, if the (U)nited States raises taxes, then (M)exico stabilizes its currency.
- Either (G)uatemala does not end its civil war or, if (H)onduras reduces poverty then so does (N)icaragua.
- Either (S)pain or (P)ortugal combats air pollution given that both (G)ermany and (A)ustria do not improve water quality.