Tutorial Contents Tutorial Two: Propositional Calculus: Language - Truth Functors - The Propositional Language - "Implicate" - Stand-alone sentences - Scope More Tutorials One Three Four Five Six Seven

## 1.

In each of the following, say whether the second sentence is an acceptable translation of the first. (If it isn't, think of situation in which the sentences would have different truth-values.)
(i) John was happy if Liverpool won the cup. [Liverpool won the cup ® John was happy].
(ii) John doesn't know if Liverpool won the cup. [Liverpool won the cup ® John doesn't know].
(iii) You won't succeed without trying. [¬you will try ® ¬you will succeed].
(iv) You will succeed only if you try. [you will try ® you will succeed].
(v) You won't succeed unless you try. [¬you will try ® ¬you will succeed].
(vi) If my mother telephones, I shall be in the garden. [My mother will telephone ® I shall be in the garden].
(vii) If that egg has been boiled for ten minutes, it is hard. [That egg has been boiled for ten minutes ® that egg is hard].
(viii)  If an egg has been boiled for ten minutes, it is hard. [An egg has been boiled for ten minutes ® an egg is hard].
(ix) If that egg had been boiled for ten minutes, it would have been soft. [That egg was boiled for ten minutes ® that egg was soft].