Let P = {-1} and Q = {-7, -5, -3, -1, 1}. What is P ∪ Q? Choices: (A){-1} (B){-5, -3} (C){-7, -5, -3, -1, 1} (D){-7, -5, -3, 1}

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

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

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Math Problems

Algebra 1

Unions and intersections of sets

Full solution

Q. Let

P = \{-1\}

and

Q = \{-7, -5, -3, -1, 1\}

. What is

P \cup Q

\newline

Choices:

\newline

(A)

\{-1\}

\newline

(B)

\{-5, -3\}

\newline

(C)

\{-7, -5, -3, -1, 1\}

\newline

(D)

\{-7, -5, -3, 1\}

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