Question

The correct symbolization of the proposition 'Some flowers are red.' in the form of Predicate calculus is:

• A. (∃x)(Fx ⊃ Rx)
• B. (∀x)(Fx · Rx)
• C. (∃x)(Fx ⊃ Rx)
• D. (∃x)(Fx · Rx)

Hint:

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.

Answer 1

The Correct Option is C

Step 1: Understanding the Proposition.
The proposition "Some flowers are red" is a statement involving an existential quantifier because it talks about the existence of at least one red flower. In predicate logic, we express this as "There exists some flower such that it is red."
Step 2: Analyzing the Options.
- 1. \( (\exists x)(Fx \supset Rx) \): This is incorrect because it uses the implication (\(\supset\)), which does not correctly express the existence of a flower being red. - 2. \( (\forall x)(Fx \cdot Rx) \): This is incorrect because it uses a universal quantifier (\(\forall\)) which is not suitable for expressing "some" flowers. - 3. \( (\exists x)(Fx \supset Rx) \): This is correct. The symbolization correctly uses the existential quantifier (\(\exists x\)) to express that some flower \(x\) is red (\(Fx \supset Rx\)). - 4. \( (\exists x)(Fx \cdot Rx) \): This is incorrect because it uses conjunction (\(\cdot\)) instead of an implication.
Step 3: Conclusion. The correct answer is 3. \( (\exists x)(Fx \supset Rx) \).
Final Answer: \[ \boxed{\text{The correct answer is 3. } (\exists x)(Fx \supset Rx)} \]