If C = {x | x is an even integer}, what is the power set of C?

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Question: If C = {x | x is an even integer}, what is the power set of C?

Options:

Correct Answer: Infinite

Solution:

The power set of an infinite set is also infinite. Since C contains all even integers, its power set is infinite.

If C = {x | x is an even integer}, what is the power set of C?

If C = {x | x is an even integer}, what is the power set of C?

Step 1: Understand what set C is. C is the set of all even integers, like -4, -2, 0, 2, 4, 6, and so on.
Step 2: Know what a power set is. The power set of a set is the set of all possible subsets of that set.
Step 3: Realize that C is an infinite set because there are infinitely many even integers.
Step 4: Understand that the power set of an infinite set is also infinite. This means it has infinitely many subsets.
Step 5: Conclude that since C is infinite, its power set is also infinite.

Power Set – The power set of a set is the set of all possible subsets, including the empty set and the set itself.
Infinite Sets – An infinite set has an unbounded number of elements, and its power set is also infinite.
Even Integers – Even integers are integers that are divisible by 2, forming an infinite set.