Given that Z = {1,2,4,5} what is the power of set Z?

Analysis

The question asks for the "power of set Z," which is mathematically referred to as the Power Set of Z. Specifically, it asks for the number of elements in the power set of Z.

Concept

The Power Set of a set is the set of all possible subsets of that set, including the empty set ($\emptyset$) and the set itself.

To find the number of elements in a power set, we use the formula:

Where:

• $n$ is the number of elements in the original set $Z$.
• $n(P(Z))$ is the total number of subsets (the power of the set).

Solution

1. Identify the number of elements in set Z: The set $Z = \{1, 2, 4, 5\}$. Counting the elements, we see there are 4 elements. Therefore, $n = 4$.

2. Apply the formula: Substitute $n = 4$ into the formula $2^n$: $$2^4 = 2 \times 2 \times 2 \times 2$$

3. Calculate the result: $2 \times 2 = 4$ $4 \times 2 = 8$ $8 \times 2 = 16$

The total number of subsets (the power of the set) is 16.

Conclusion

Comparing our result to the given options: A. 16 B. 8 C. 10 D. 12

The correct option is A.

Exam Tip

Whenever you see a question asking for the "power of a set," don't get confused by the terminology. Just count the number of items in the curly brackets and raise 2 to the power of that count. If the set has 3 items, the answer is $2^3 = 8$; if it has 5 items, the answer is $2^5 = 32$. Always remember: 2 raised to the power of the number of elements.