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Let P={−1}P = \{-1\} and Q={−7,−5,−3,−1,1}Q = \{-7, -5, -3, -1, 1\}. What is P∪QP \cup Q?\newlineChoices:\newline(A) {−1}\{-1\}\newline(B) {−5,−3}\{-5, -3\}\newline(C) {−7,−5,−3,−1,1}\{-7, -5, -3, -1, 1\}\newline(D) {−7,−5,−3,1}\{-7, -5, -3, 1\}

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Q. Let P={−1}P = \{-1\} and Q={−7,−5,−3,−1,1}Q = \{-7, -5, -3, -1, 1\}. What is P∪QP \cup Q?\newlineChoices:\newline(A) {−1}\{-1\}\newline(B) {−5,−3}\{-5, -3\}\newline(C) {−7,−5,−3,−1,1}\{-7, -5, -3, -1, 1\}\newline(D) {−7,−5,−3,1}\{-7, -5, -3, 1\}
  1. Concept of Union: Understand the concept of union of sets.\newlineThe union of two sets PP and QQ, denoted by P∪QP \cup Q, is the set of all elements that are in PP, or in QQ, or in both. It includes all the unique elements from both sets.
  2. Identify Elements: Identify the elements of set PP and set QQ. We have P={−1}P = \{-1\} and Q={−7,−5,−3,−1,1}Q = \{-7, -5, -3, -1, 1\}.
  3. Combine for Union: Combine the elements of PP and QQ to form the union.\newlineSince the union includes all unique elements, we combine the elements of both sets without repeating any elements.\newlineP∪Q={−7,−5,−3,−1,1}P \cup Q = \{-7, -5, -3, -1, 1\}.
  4. Check Correct Answer: Check the answer choices to find the correct union. Comparing our result with the given choices, we find that: (A) {−1}\{-1\} is not correct because it only includes elements from PP. (B) {−5,−3}\{-5, -3\} is not correct because it is missing elements from both PP and QQ. (C) {−7,−5,−3,−1,1}\{-7, -5, -3, -1, 1\} is correct because it includes all unique elements from both PP and QQ. (D) {−7,−5,−3,1}\{-7, -5, -3, 1\} is not correct because it is missing −1-1, which is in both PP and QQ.

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