Question

Let set A= { 2,3,4,5,6}

Let set B - { a,b,c,d,2,3}

Find the following:

1. A U B

2. A - B

Answer 1

`\displaystyle{1.) \, A \cup B = \{2,3,4,5,6,a,b,c,d\} }\\\\\displaystyle{2.) \, A-B = \{ 4,5,6 \}}`

Explanation:

Given two sets which are:

`\displaystyle{A = \{2,3,4,5,6\} }\\\\\displaystyle{B= \{a,b,c,d,2,3\} }`

To find
`\displaystyle{A \cup B}` (A union B), we will simply merge both sets together - basically add all elements into one set. Therefore:

`\displaystyle{A \cup B = \{2,3,4,5,6,a,b,c,d,2,3\} }`

However, we do not write duplicate elements in set so we will have to take one of duplicates out. We will be able to rewrite the union set above as:

`\displaystyle{A \cup B = \{2,3,4,5,6,a,b,c,d\} }`

To find
`\displaystyle{A-B}` (A minus B), we will only take elements that are apart of set A.
This means that if an element is in set A and not in set B then that element will be apart of A - B.
On the other hand, if an element is in set A but if it's also in set B then it'll be cleared out as A - B states that it'll only take in elements that are apart of set A and being apart of both sets will not count in.

Thus, 2 and 3 are not counted in since they are also apart of set B too although they both are apart of set A.

Therefore:

`\displaystyle{A-B = \{ 4,5,6 \}}`