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Let \( A = \{71, 18, 91, 50, 74, 52\} \).

Select all sets that are subsets of \( A \).

A. \( D = \{50, 71, 52, 18, 74, 25, 91\} \)

B. \( F = \{74, 50, 52, 18, 71, 40\} \)

C. \( H = \{91, 50, 71, 74\} \)

D. \( C = \{71, 52, 18, 91, 74, 50\} \)

E. \( E = \{74, 91, 71, 18, 50\} \)

F. \( G = \{52, 18, 50, 80, 71\} \)

Answer :

Final answer:

The subsets of the given set A are H, C, and E. These subsets include only numbers found in set A and do not include any numbers not found in set A.

Explanation:

In the subject of Mathematics, specifically set theory, a subset is a set where all of its elements are also elements of another, larger set. In this question, we are given our larger set as A={71,18,91,50,74,52} and asked to identify its subsets:

  1. D={50,71,52,18,74,25,91}
  2. F={74,50,52,18,71,40}
  3. H={91,50,71,74}
  4. C={71,52,18,91,74,50}
  5. E={74,91,71,18,50}
  6. G={52,18,50,80,71}

Analyzing each option, we can see that a subset must only include numbers that are present in set A, and should not include any numbers not found in set A. So, our subsets of A are: H={91,50,71,74}, C={71,52,18,91,74,50}, and E={74,91,71,18,50}. It's important to note that the numbers within the subsets do not have to be in the same order as they are in set A.

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