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How many subsets can be formed from the set C = {x, y, z, w}?

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Question: How many subsets can be formed from the set C = {x, y, z, w}?

Options:

  1. 4
  2. 8
  3. 16
  4. 2

Correct Answer: 8

Solution: 

The number of subsets of a set with n elements is 2^n. Here, n = 4, so 2^4 = 16.

How many subsets can be formed from the set C = {x, y, z, w}?

Practice Questions

Q1
How many subsets can be formed from the set C = {x, y, z, w}?
  1. 4
  2. 8
  3. 16
  4. 2

Questions & Step-by-Step Solutions

How many subsets can be formed from the set C = {x, y, z, w}?
Correct Answer: 16
  • Step 1: Identify the set C, which is {x, y, z, w}.
  • Step 2: Count the number of elements in the set C. There are 4 elements: x, y, z, and w.
  • Step 3: Use the formula for the number of subsets, which is 2^n, where n is the number of elements in the set.
  • Step 4: Substitute the value of n into the formula. Here, n = 4, so we calculate 2^4.
  • Step 5: Calculate 2^4, which equals 16.
  • Step 6: Conclude that the number of subsets that can be formed from the set C is 16.
  • Subsets – A subset is a set formed from the elements of another set, including the empty set and the set itself.
  • Power Set – The power set of a set is the set of all possible subsets, including the empty set and the set itself.
  • Exponential Growth – The number of subsets grows exponentially with the number of elements in the set, specifically as 2^n.
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