A PREDICATE $P(x)$ is
Aa statement always evaluating to TRUE
Ba statement always evaluating to FALSE
Ca statement whose truth depends on $x$
Dthe name of a logical quantifier
Answer & Solution
Correct answer: C. a statement whose truth depends on $x$
1. A PREDICATE is a statement containing one or more VARIABLES whose truth value depends on the value(s) of the variable(s).
2. Example: $P(x) = '\,x$ is even'. Then $P(4) = $ TRUE; $P(7) = $ FALSE.
3. Predicates become STATEMENTS (definite truth values) when:
- Specific values are plugged in: $P(4)$, $P(7)$.
- QUANTIFIERS are applied: $\forall x\, P(x)$, $\exists x\, P(x)$.
4. Options A, B describe constants, not predicates. Option D confuses predicates with quantifiers.
_Source: Oscar Levin, "Discrete Mathematics: An Open Introduction", §0.3 (Predicates and Quantifiers)._
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