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Let D={5}D = \{5\} and E={5,15,25,35}E = \{5, 15, 25, 35\}. What is DED \cup E?\newlineChoices:\newline(A){5,15,25,35}\{5, 15, 25, 35\}\newline(B){15,25,35}\{15, 25, 35\}\newline(C){25}\{25\}\newline(D) \emptyset

Full solution

Q. Let D={5}D = \{5\} and E={5,15,25,35}E = \{5, 15, 25, 35\}. What is DED \cup E?\newlineChoices:\newline(A){5,15,25,35}\{5, 15, 25, 35\}\newline(B){15,25,35}\{15, 25, 35\}\newline(C){25}\{25\}\newline(D) \emptyset
  1. Initialize Sets: D={5}D = \{5\} and E={5,15,25,35}E = \{5, 15, 25, 35\}. To find the union of two sets, we combine all the unique elements from both sets.
  2. Find Union: The union of DD and EE, denoted by DED \cup E, will include all the elements from DD and all the elements from EE without repeating any elements.
  3. Combine Unique Elements: Since 55 is present in both DD and EE, it will only be listed once in the union. The rest of the elements from EE will be included as they are not present in DD.
  4. Final Union: Therefore, DE={5,15,25,35}D \cup E = \{5, 15, 25, 35\}.
  5. Correct Answer: Comparing the result with the given choices, we find that the correct answer is (A)5,15,25,35{5, 15, 25, 35}.

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