Math Problem Statement

Give me some exercises for set theory

Solution

Here are five exercises related to set theory:

  1. Basic Set Operations
    Let A={1,2,3,4}A = \{1, 2, 3, 4\}, B={3,4,5,6}B = \{3, 4, 5, 6\}, and C={1,5,6,7}C = \{1, 5, 6, 7\}.
    Find:

    • ABA \cup B (union of AA and BB)
    • ABA \cap B (intersection of AA and BB)
    • ABA - B (difference between AA and BB)
    • A(BC)A \cap (B \cup C)
  2. Subset Verification
    Given X={1,2,3,4,5,6}X = \{1, 2, 3, 4, 5, 6\} and Y={2,4,6}Y = \{2, 4, 6\}, determine if:

    • YXY \subseteq X (Is YY a subset of XX?)
    • XYX \subset Y (Is XX a subset of YY?)
  3. Power Set
    Find the power set of P={a,b}P = \{a, b\}.
    (Hint: The power set is the

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Set Theory
Union
Intersection
Subsets
Power Set

Formulas

A ∪ B (Union of sets A and B)
A ∩ B (Intersection of sets A and B)
A - B (Difference between sets A and B)

Theorems

Subset Theorem (Y ⊆ X if all elements of Y are in X)
Power Set Theorem (The power set of a set P is the set of all subsets of P)

Suitable Grade Level

Grades 9-12