Discussion
How many models satisfy a sentence with 3 symbols that is true in exactly half of them?
Answer: C
Three symbols give eight models altogether, so half of them is:
\[ \tfrac{8}{2} = 4 \]
that is 4 models. A sentence true in every model would be valid and one true in none unsatisfiable, so this sentence is contingent. Counting models is the most direct way to see the difference between the three semantic categories, and it is worth doing once explicitly on a small example.
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