Let P and Q be two non-void relations on a set A. Which of the following statements are correct? I. P and Q are reflexive \Rightarrow P\cap Q is reflexive. II. P and Q are symmetric \Rightarrow P\cup Q is symmetric. III. P and Q are transitive \Rightarrow P\cap Q is transitive. Select the answer using the code given below.
- A. I and II only
- B. II and III only
- C. I and III only
- D. I, II and III ✓
Correct Answer: D. I, II and III
Explanation
The intersection of two reflexive relations is always reflexive. The union of two symmetric relations is always symmetric. The intersection of two transitive relations is always transitive. Thus, all three statements represent mathematically valid properties of relations.
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