Exploring Sets: Computing A - B, B x C, AB and A(B-A)

• sapiental
In summary, exploring sets in computing A-B allows us to find the elements present in set A but not in set B. B x C is computed by multiplying each element in set B with every element in set C, resulting in a new set of ordered pairs. Computing AB results in a new set containing all possible combinations of elements from set A and set B, also known as the Cartesian product. A(B-A) is computed by finding the difference between set A and set B and then computing the Cartesian product between set A and the resulting set. Some real-life applications of computing sets include data analysis, statistical modeling, computer programming, and various fields such as genetics, economics, and linguistics.

Homework Statement

Let A = {1,3,5,6}, B = {3,5} and C = {a,b,c}

Compute

a. A - B
b. B x C (cartesian product)
c. AB
d. A(B-A)

Homework Equations

Table of set computation in text

The Attempt at a Solution

a. = {1,6}
b. = {(1,3,a),(1,3,b),(1,3,c),(1,5,a),(1,5,b),(1,5,c),(3,3,a),(3,3,b),(3,3,c),(3,5,a),(3,5,b),(3,5,c),
(5,3,a),(5,3,b),(5,3,c),(5,5,a),(5,5,b),(5,5,c),(6,3,a),(6,3,b),(6,3,c),(6,5,a),(6,5,b),(6,5,c)}
c. = {3,5}
d. = null set

First time working with sets, any support helps. Thanks!

looks good, provided b. asks you to compute A x B x C and not B x C

thanks!

1. What is the purpose of exploring sets in computing A-B?

The purpose of exploring sets in computing A-B is to find the elements that are present in set A but not in set B. This operation is also known as the set difference.

2. How is B x C computed?

B x C is computed by taking each element in set B and multiplying it with every element in set C, resulting in a new set of all possible ordered pairs.

3. What is the result of computing AB?

The result of computing AB is a new set containing all possible combinations of elements from set A and set B. This is also known as the Cartesian product of two sets.

4. How is A(B-A) computed?

A(B-A) is computed by first finding the difference between set A and set B, and then computing the Cartesian product between set A and the resulting set. This will result in a new set containing all the elements in set A that are not in set B, paired with all elements in set A.

5. What are some real-life applications of computing sets?

Some real-life applications of computing sets include data analysis, statistical modeling, and computer programming. Sets are also used in various fields such as genetics, economics, and linguistics to organize and analyze data.