First Translation Exercise
Answers (first 10)
Translate the following English sentences into Propositional Logic. Use ">" for the horseshoe and "iff" for the triplebar.
1. My father taught me to work, but not to love it. (Abraham Lincoln).
A: My father taught me to work. B: My father taught me to love work.
(A & ~B)
2. Kindness is in our power, but fondness is not. (Samuel Johnson) A: Kindness is in our power B: Fondness is in our power.
3. But if you wisely invest in beauty, it will remain with you all the days of your life. (Frank Lloyd Wright)
A: You wisely invest in beauty. B: Beauty will remain with you all the days of our life.
(A ⊃ B)
4. It is not poetry, if it make no appeal to our passions or our imagination. (Samuel Taylor Coleridge)
A: It is poetry. B: It appeals to our passions. C: It appeals to our imagination.
(~B & ~C) ⊃ ~A
or translate as:
~(B v C) ⊃ ~A
5. Size is not grandeur, and territory does not make a nation. (Thomas H. Huxley) A: Size is grandeur B: Territory makes a nation.
(~A & ~B)
6. If you build a castle in the air, you won't need a mortgage. (Philip Lazarus) A: You build a castle in the air B: You need a mortgage.
(A ⊃ ~B)
7. The mind itself, like other things, must sometimes be unbent or else it will be either weakened or broken. (Philip Sidney)
A: The mind must sometimes be unbent. B: The mind will be weakened. C: The mind will be broken. (A v (B v C))
8. If you don't get what you want, it is a sign either that you did not seriously want it, or that you tried to bargain over the price. (R. Kipling) A: You get what you want. B: It is a sign that you did seriously want it. C: It is a sign that you tried to bargain over the price. (~A ⊃ (~B v C))
9. The forces of a capitalist society, if left unchecked, tend to make the rich richer and the poor poorer. (J. Nehru) A: The forces of a capitalist society are checked. B: The forces of a capitalist society tend to make the rich richer. C: The forces of a capitalist society tend to make the poor poorer.
(~A ⊃ (B & C))
10. Action does not always bring happiness, but there is no happiness without it. ( Benjamin Disraeli)
A: Action always brings happiness. B: There is happiness without action.