Math Problem Statement

If P = {-2, 0, 2, 4, 6} and Q = {-3, -1, 0, 2, 3, 5}, find the set P ∩ Q.

Solution

The problem states:

Given two sets P={2,0,2,4,6}P = \{-2, 0, 2, 4, 6\} and Q={3,1,0,2,3,5}Q = \{-3, -1, 0, 2, 3, 5\}, find the intersection of PP and QQ, denoted as PQP \cap Q.

Solution:

The intersection of two sets PQP \cap Q includes only the elements that are common to both sets PP and QQ.

  1. Set P={2,0,2,4,6}P = \{-2, 0, 2, 4, 6\}
  2. Set Q={3,1,0,2,3,5}Q = \{-3, -1, 0, 2, 3, 5\}

Now, let's find the common elements:

  • Both sets contain 00 and 22.

Thus, the intersection of PP and QQ is: PQ={0,2}P \cap Q = \{0, 2\}

Would you like further details or have any questions?

Here are 5 related questions:

  1. How do you find the union of two sets?
  2. What is the complement of a set?
  3. How can Venn diagrams help visualize set operations?
  4. What is the difference between intersection and union in set theory?
  5. How do you find the difference between two sets?

Tip: In set theory, the intersection operation is commutative, meaning PQ=QPP \cap Q = Q \cap P.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Intersection of Sets

Formulas

P ∩ Q = {x | x ∈ P and x ∈ Q}

Theorems

Commutative Property of Intersection

Suitable Grade Level

Grades 6-8