Discussion
How many rows does a truth table for 4 proposition symbols have?
Answer: B
Each symbol takes two values independently, so the count is:
\[ 2^{4} = 16 \]
giving 16 rows. Twenty symbols would give over a million and thirty over a billion, which is why truth tables are a definition rather than an algorithm. That the semantics is defined by an exponentially large object, while practical reasoning must avoid constructing it, is the tension every inference procedure addresses.
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