Math Problem Statement

Let the Universal set be the letters a through j: U = {a, b, ..., i, j}.

Let A = {a, b, c, g}, B = {b, f, g, h}, and C = {c, d, f, g}

List the elements of the set A∩(B∪C)

Solution

To find the elements of the set A(BC)A \cap (B \cup C), we'll follow these steps:

Step 1: Find BCB \cup C

The union of sets BB and CC (denoted BCB \cup C) includes all elements that are in either BB or CC:

B={b,f,g,h}B = \{b, f, g, h\} C={c,d,f,g}C = \{c, d, f, g\}

So,

BC={b,c,d,f,g,h}B \cup C = \{b, c, d, f, g, h\}

Step 2: Find A(BC)A \cap (B \cup C)

Now, we find the intersection of set AA with BCB \cup C. The intersection (denoted A(BC)A \cap (B \cup C)) includes all elements that are in both AA and BCB \cup C:

A={a,b,c,g}A = \{a, b, c, g\} BC={b,c,d,f,g,h}B \cup C = \{b, c, d, f, g, h\}

The common elements between AA and BCB \cup C are bb, cc, and gg.

Thus,

A(BC)={b,c,g}A \cap (B \cup C) = \{b, c, g\}

So, the elements of the set A(BC)A \cap (B \cup C) are:

{b,c,g}\boxed{\{b, c, g\}}

Do you need any more details or have any questions?


  1. How would you find A(BC)A \cup (B \cap C)?
  2. What is the complement of set AA with respect to UU?
  3. Can you list the elements of ABCA \cap B \cap C?
  4. How do you determine the difference ABA - B?
  5. What would be the result of A(BC)A \cup (B \cup C)?

Tip: The union of sets combines all unique elements, while the intersection selects only the elements common to both sets.

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Math Problem Analysis

Mathematical Concepts

Set theory
Union
Intersection
Complement

Formulas

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Theorems

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Suitable Grade Level

High school