Question

1. which of the following sets is an infinite set?

a = {1, 2, 4, 8, 16...}
k = {-1, -4, -7, -10, -13, -17}
d = {2, 4, 6, 8, 10, 12}
y = {1, 3, 5, 7, 9}

Explanation:

Step1: Define infinite set

An infinite set is a set that has an unlimited number of elements (it can't be counted completely). A finite set has a fixed, countable number of elements.

Step2: Analyze set A

Set \( A = \{1, 2, 4, 8, 16...\} \). The "..." indicates that the pattern (each term is multiplied by 2: \( 1\times2 = 2 \), \( 2\times2 = 4 \), \( 4\times2 = 8 \), etc.) continues indefinitely. So, it has infinitely many elements.

Step3: Analyze set K

Set \( K = \{-1, -4, -7, -10, -13, -17\} \). Let's check the number of elements: we can count them, and there are 6 elements. So, it's finite.

Step4: Analyze set D

Set \( D = \{2, 4, 6, 8, 10, 12\} \). We can count the elements: there are 6 elements. So, it's finite.

Step5: Analyze set Y

Set \( Y = \{1, 3, 5, 7, 9\} \). We can count the elements: there are 5 elements. So, it's finite.

Answer:

A. \( A = \{1, 2, 4, 8, 16...\} \)