Suppose A = {5,6,8,10,12} and B = {8,9,12,13,14}

What is AunionB?

A ∪ B = {5, 6, 8, 9, 10, 12, 13, 14}

Step-by-step explanation:

The symbol of union is ∪

The symbol of intersection is ∩

In the sets A and B

A ∪ B means all elements in sets A and B without repeating

A ∩ B means the common elements in sets A and B

n (A ∪ B) = n (A) + n (B) - n (A ∩B), where n is the number of elements in the set

Now let us solve the question

∵ Set A = {5, 6, 8, 10, 12}

∴ n (A) = 5

∵ Set B = {8, 9, 12, 13, 14}

∴ n (B) = 5

The elements 8 and 12 are in the two sets

∵ There are two common elements in the two sets 8 and 12

∴ n (A ∩ B) = 2

Use the 3rd rule above to find how many elements in A ∪ B

∵ n (A ∪ B) = 5 + 5 - 2

∴ n (A ∪ B) = 8

∴ The set of A ∪ B has 8 elements

∵ A ∪ B means all elements in A and B without repeating

∴ A ∪ B = {5, 6, 8, 9, 10, 12, 13, 14}