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:

An infinite set is a set that has an unlimited number of elements. Let's analyze each set:

• Set \( A = \{1, 2, 4, 8, 16...\} \): The pattern here is \( 2^0, 2^1, 2^2, 2^3, 2^4... \), so it continues indefinitely, meaning it has infinitely many elements.
• Set \( K = \{-1, -4, -7, -10, -13, -17\} \): This set has a finite number of elements (6 elements), so it's a finite set.
• Set \( D = \{2, 4, 6, 8, 10, 12\} \): This set has 6 elements, so it's a finite set.
• Set \( Y = \{1, 3, 5, 7, 9\} \): This set has 5 elements, so it's a finite set.

Answer:

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