Question

which diagram represents the following sets? p = {x | x is an integer divisible by 2}; q = {x | x is an odd integer}; r = {x | x is an integer divisible by 3}

Explanation:

Step1: Analyze Set Properties

• \( P \): Integers divisible by 2 (even integers).
• \( Q \): Odd integers.
• \( R \): Integers divisible by 3.

• \( P \) and \( Q \) are disjoint (no number is both even and odd), so their circles should not overlap.
• \( P \) and \( R \) overlap (e.g., 6 is divisible by 2 and 3).
• \( Q \) and \( R \) overlap (e.g., 9 is odd and divisible by 3).

Step2: Evaluate Diagrams

• First Diagram: \( P \) and \( Q \) are disjoint (good), \( P \) and \( R \) overlap (good), \( Q \) and \( R \) overlap (good).
• Second Diagram: \( P \) and \( Q \) overlap (bad, since even and odd are disjoint).
• Third Diagram: \( P \) and \( Q \) overlap (bad, same reason).

Answer:

The Left Diagram (First Diagram)