The correct symbolization of the proposition 'Some flowers are red.' in the form of Predicate calculus is:
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In predicate logic, existential quantifiers (\(\exists\)) are used to express the existence of at least one element, while universal quantifiers (\(\forall\)) are used for all elements.
Step 1: Understand the Proposition. The statement "Some flowers are red" indicates the existence of at least one red flower. In predicate logic, this is represented as: "There exists some flower such that it is red." Step 2: Analyze Options. - 1. \( (\exists x)(Fx \supset Rx) \): Incorrect. The implication (\(\supset\)) does not accurately convey that a flower is red. - 2. \( (\forall x)(Fx \cdot Rx) \): Incorrect. The universal quantifier (\(\forall\)) is not suitable for "some." - 3. \( (\exists x)(Fx \supset Rx) \): Correct. The existential quantifier (\(\exists x\)) is used, and the expression correctly symbolizes "some flower \(x\) is red" via \(Fx \supset Rx\). - 4. \( (\exists x)(Fx \cdot Rx) \): Incorrect. Conjunction (\(\cdot\)) is used instead of implication. Step 3: Conclusion. Option 3 is the correct symbolization: \( (\exists x)(Fx \supset Rx) \). Final Answer: \[ \boxed{\text{The correct answer is 3. } (\exists x)(Fx \supset Rx)} \]