Truth-functional Propositions in QL
So far we've looked at singular propositions, simple
quantified propositions and their negations. But we can also create complex
propositions out of singular propositions, quantified propositions and their
negations using our good-old sentential operators. Since our operators work on
any proposition, we can certainly use them here.
Consider the English sentence:
| If Blanche is studious, then everyone is. |
We can begin by making the second simple sentence contained in (1) explicit:
| If Blanche is studious, then everyone is studious. |
The sentence is a conditional. The antecedent is a singular proposition, and the consequent is a simple universally quantified sentence. Using "Sx" as the propositional function "x is studious" and "b" for "Blanche" we have:
| Sb ⊃ (x)Sx |
Easy! We're just connecting sentences with our well-known propositional connectives. Here's a translation exercise to practice this easy skill.
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