Question

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

Answer 1

Answer:

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}