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Let Q={−8}Q = \{-8\} and R={−12,−4,6,8,14}R = \{-12, -4, 6, 8, 14\}. What is Q∪RQ \cup R?\newlineChoices:\newline(A) {6,8,14}\{6, 8, 14\}\newline(B) ∅\emptyset \newline(C) {−12,6}\{-12, 6\}\newline(D) {−12,−8,−4,6,8,14}\{-12, -8, -4, 6, 8, 14\}

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Q. Let Q={−8}Q = \{-8\} and R={−12,−4,6,8,14}R = \{-12, -4, 6, 8, 14\}. What is Q∪RQ \cup R?\newlineChoices:\newline(A) {6,8,14}\{6, 8, 14\}\newline(B) ∅\emptyset \newline(C) {−12,6}\{-12, 6\}\newline(D) {−12,−8,−4,6,8,14}\{-12, -8, -4, 6, 8, 14\}
  1. Find Union of Sets: We need to find the union of sets QQ and RR. The union of two sets is the set containing all the elements from both sets, without duplicates.Q={−8}Q = \{-8\}R={−12,−4,6,8,14}R = \{-12, -4, 6, 8, 14\}To find Q∪RQ \cup R, we combine all the elements from both sets.
  2. List Unique Elements: We list all the unique elements from both sets QQ and RR.Q∪R={−12,−8,−4,6,8,14}Q \cup R = \{-12, -8, -4, 6, 8, 14\}We make sure not to include any duplicates and to list each element only once.
  3. Check Given Choices: Now we check the choices given to see which one matches our result.\newline(A) {6,8,14}\{6, 8, 14\} does not include all the elements from Q∪RQ \cup R.\newline(B) ∅\emptyset is the empty set and does not match Q∪RQ \cup R.\newline(C) {−12,6}\{-12, 6\} is missing several elements from Q∪RQ \cup R.\newline(D) {−12,−8,−4,6,8,14}\{-12, -8, -4, 6, 8, 14\} matches our calculated union of QQ and RR.

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