Question

week 7: introduction to pro...
current objective
using and, or, and not notation to describe events
question
a lawyer has numbered the cases that he is working on. he has criminal cases numbered 1, 2, 3, 4 and civil numbered 1, 2, 3, 4, 5. let r be the event of selecting a criminal case, c the event of selecting a civil case, e the event of selecting an even - numbered case, and o the event of selecting an odd case.
selecting the criminal case number 4 is an example of which of the following events? select all correct answers.

Explanation:

To solve this, we analyze the event of selecting criminal case number 4:

Step 1: Analyze event \( R \) (criminal case)

Case 4 is a criminal case (since criminal cases are numbered 1,2,3,4), so it belongs to \( R \).

Step 2: Analyze event \( E \) (even - numbered case)

The number 4 is even (as \( 4\div2 = 2 \), with no remainder), so it belongs to \( E \).

Step 3: Analyze event \( C \) (civil case)

Civil cases are numbered 1,2,3,4,5? Wait, no—the problem says: “criminal cases numbered 1,2,3,4 and civil numbered 1,2,3,4,5”? Wait, re - reading: “He has criminal cases numbered 1,2,3,4 and civil numbered 1,2,3,4,5.” Wait, but case 4: is it criminal or civil? Wait, the lawyer has criminal cases 1 - 4 and civil cases 1 - 5. So case 4: is it both? Wait, no—probably a typo, but the problem says “selecting the criminal case number 4”. So case 4 is criminal, so not civil (since civil cases are a separate set? Wait, maybe the civil cases are numbered 1 - 5, and criminal 1 - 4. So case 4 is criminal (so \( R \)) and even - numbered ( \( E \) ), not civil ( \( C \) ) and not odd ( \( O \), since 4 is even).

So the events that include selecting criminal case number 4 are \( R \) (criminal case) and \( E \) (even - numbered case). If we consider the intersection \( R\cap E \) (criminal AND even - numbered), that is also correct, but the question says “select all correct answers” (the options are not fully shown, but from analysis:

• \( R \): Yes, because it is a criminal case.
• \( E \): Yes, because 4 is even.
• \( R\cap E \): Yes, because it is a criminal AND even - numbered case.
• \( C \): No, because it is a criminal case (not civil).
• \( O \): No, because 4 is even (not odd).

If we assume the options include \( R \), \( E \), and \( R\cap E \), those are correct.

Answer:

To solve this, we analyze the event of selecting criminal case number 4:

Step 1: Analyze event \( R \) (criminal case)

Case 4 is a criminal case (since criminal cases are numbered 1,2,3,4), so it belongs to \( R \).

Step 2: Analyze event \( E \) (even - numbered case)

The number 4 is even (as \( 4\div2 = 2 \), with no remainder), so it belongs to \( E \).

Step 3: Analyze event \( C \) (civil case)

Civil cases are numbered 1,2,3,4,5? Wait, no—the problem says: “criminal cases numbered 1,2,3,4 and civil numbered 1,2,3,4,5”? Wait, re - reading: “He has criminal cases numbered 1,2,3,4 and civil numbered 1,2,3,4,5.” Wait, but case 4: is it criminal or civil? Wait, the lawyer has criminal cases 1 - 4 and civil cases 1 - 5. So case 4: is it both? Wait, no—probably a typo, but the problem says “selecting the criminal case number 4”. So case 4 is criminal, so not civil (since civil cases are a separate set? Wait, maybe the civil cases are numbered 1 - 5, and criminal 1 - 4. So case 4 is criminal (so \( R \)) and even - numbered ( \( E \) ), not civil ( \( C \) ) and not odd ( \( O \), since 4 is even).

So the events that include selecting criminal case number 4 are \( R \) (criminal case) and \( E \) (even - numbered case). If we consider the intersection \( R\cap E \) (criminal AND even - numbered), that is also correct, but the question says “select all correct answers” (the options are not fully shown, but from analysis:

• \( R \): Yes, because it is a criminal case.
• \( E \): Yes, because 4 is even.
• \( R\cap E \): Yes, because it is a criminal AND even - numbered case.
• \( C \): No, because it is a criminal case (not civil).
• \( O \): No, because 4 is even (not odd).

If we assume the options include \( R \), \( E \), and \( R\cap E \), those are correct.