Question

chapter 1 quiz
score: 18/100 answered: 3/15
question 4
consider the set ( s = {3, 5, 7, 9, dots} ). which of the following is an element of ( s )?
1
13
10
20

Explanation:

Step1: Analyze the set S

The set \( S = \{3, 5, 7, 9, \dots\} \) represents the set of odd integers starting from 3. An odd integer is a number that is not divisible by 2, i.e., when divided by 2, it leaves a remainder of 1. The general form of an element in this set can be considered as \( 2n + 1 \) where \( n \geq 1 \) (since when \( n = 1 \), \( 2(1)+1 = 3 \); \( n = 2 \), \( 2(2)+1 = 5 \), and so on).

Step2: Check each option

• Option 1: Let's see if 1 can be part of the set. If we use the formula \( 2n + 1 = 1 \), then \( 2n=0 \) which gives \( n = 0 \). But our set starts from \( n = 1 \) (since the first element is 3 when \( n = 1 \)), so 1 is not in the set \( S \).
• Option 13: Let's check if 13 follows the pattern. Using the formula \( 2n + 1 = 13 \), we solve for \( n \): \( 2n=13 - 1=12 \), so \( n = 6 \). Since \( n = 6 \) is a positive integer, 13 is in the set \( S \) (as \( 2(6)+1 = 13 \)).
• Option 10: 10 is an even number (since \( 10\div2 = 5 \) with remainder 0), so it cannot be in the set of odd numbers starting from 3.
• Option 20: 20 is also an even number ( \( 20\div2=10 \) with remainder 0), so it is not in the set \( S \).

Answer:

13 (corresponding to the option with 13, i.e., the second option: 13)