Math Problem Statement

Consider the following sets:

  1. U=/x/x is a whole number from 0 to 20.

  2. X= /x/ x is a whole number less than 10

  3. Y=/x/x is a whole number greater than 5 but less than 20.

  4. Z=/x/x is a whole number between 4 and 11

Solution

Let's define the sets based on the information given:

  1. Set UU: The universal set consists of all whole numbers from 0 to 20.
    U={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}

  2. Set XX: This set consists of whole numbers less than 10.
    X={0,1,2,3,4,5,6,7,8,9}X = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}

  3. Set YY: This set consists of whole numbers greater than 5 but less than 20.
    Y={6,7,8,9,10,11,12,13,14,15,16,17,18,19}Y = \{6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19\}

  4. Set ZZ: This set consists of whole numbers between 4 and 11 (including 4 and 11).
    Z={4,5,6,7,8,9,10,11}Z = \{4, 5, 6, 7, 8, 9, 10, 11\}

Would you like to perform specific operations with these sets, such as union, intersection, or difference?

Here are 5 follow-up questions related to set theory:

  1. What is XYX \cup Y (the union of sets XX and YY)?
  2. What is XYX \cap Y (the intersection of sets XX and YY)?
  3. What is the complement of set ZZ with respect to UU (denoted UZU - Z)?
  4. How many elements are in the union of all three sets XX, YY, and ZZ?
  5. What is the symmetric difference between sets XX and ZZ?

Tip: The union of two sets contains all distinct elements that are in either set, while the intersection contains only elements that are in both sets.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Set Theory
Union of Sets
Intersection of Sets
Complement of Sets
Symmetric Difference

Formulas

Union of sets: X ∪ Y
Intersection of sets: X ∩ Y
Complement of sets: U - Z
Symmetric difference: (X ∪ Z) - (X ∩ Z)

Theorems

Set Union Theorem
Set Intersection Theorem
Complement Rule
Symmetric Difference Theorem

Suitable Grade Level

Grades 6-8