Math Problem Statement

List all subsets of set A = {a, b, c, d} that have 3 elements.

Solution

To list all subsets of the set A={a,b,c,d}A = \{a, b, c, d\} that have 3 elements, we need to select 3 elements out of the 4 available elements in the set.

The number of ways to choose 3 elements from a set of 4 is given by the binomial coefficient (43)\binom{4}{3}. This is equal to 4, which means there are 4 subsets of 3 elements.

The subsets of AA that have exactly 3 elements are:

  1. {a,b,c}\{a, b, c\}
  2. {a,b,d}\{a, b, d\}
  3. {a,c,d}\{a, c, d\}
  4. {b,c,d}\{b, c, d\}

These are all the possible subsets of size 3 from the set A={a,b,c,d}A = \{a, b, c, d\}.


Would you like any further explanation or examples?

Here are some related questions:

  1. How do you calculate the number of subsets of a set of any size?
  2. How do you calculate the number of subsets of size kk from a set of nn elements?
  3. What is the difference between a subset and a proper subset?
  4. How can you list all subsets of a set with more elements?
  5. How do you determine the power set of a set?

Tip: To find subsets of a set, think of each element as either being in or out of the subset. This gives you a systematic way to generate all subsets.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Set Theory
Binomial Coefficients

Formulas

Binomial Coefficient \( \binom{n}{k} = \frac{n!}{k!(n-k)!} \)

Theorems

Combinatorial subset selection

Suitable Grade Level

Grades 7-10