How To Find The Union Of Sets

Union of sets

This lesson will explain how to find the spousal relationship of sets. We will starting time with a definition of the union of two sets.

Definition: Given ii sets A and B, the union is the ready that contains elements or objects that belong to either A or to B or to both.

We write A ∪ B

Basically, we find A ∪ B by putting all the elements of A and B together. We side by side illustrate with examples.

Union of 2 sets

Case #i.

Let A = {1 orange, 1 pineapple, 1 assistant, 1 apple} and B = { 1 spoon, 1 knife, one fork}

A ∪ B = {1 orange, i pineapple, i banana, i apple tree, one spoon, ane pocketknife, one fork}

Example #2.

Find the matrimony of A and B

Union of sets A and B

A = { 1, 2, iv, vi} and B = { four, a, b, c, d, f}

A ∪ B = { 1, 2, four, 6, 4, a, b, c, d, f} = { 1, 2, 4, half-dozen, a, b, c, d, f }

Discover that it is perfectly OK to write 4 in one case or twice.

Instance #3.

A = { 10 / ten is a number bigger than 4 and smaller than 8}

B = { x / x is a positive number smaller than 7}

A = { 5, 6, 7} and B = { 1, 2, three, 4, 5, vi}

A ∪ B = { 1, ii, 3, 4, 5, 6, 7}

Or A ∪ B = { x / x is a number bigger than 0 and smaller than 8}

Again, observe that five and 6 were written only once although it would be perfectly OK to write them twice.

Case #four.

A = { x / x is a country in Asia}

B = { x / ten is a land in Africa}

A ∪ B = {x / x is a country in Asia and Africa} = { all countries in Asia and Africa}

Technically, using the definition, nosotros should accept said A ∪ B = {x / x is a country in either Asia or Africa or both countries}

Even so, in real life, this is not the way we talk. By saying all countries in Asia and Africa, it is usually understood in daily conversations that we are talking about all countries in Asia and all countries in Africa.

Instance #5.

Union of disjoint sets

A = {#, %, &, * , $ }

B = { }

A ∪ B = {#, %, &,

* , $}

You may have definitely noticed that the marriage of sets is but plant by putting the elements of the sets together, preferably without repetition.

Definition of the union of three sets

Given three sets A, B, and C the matrimony is the gear up that contains elements or objects that belong to either A, B, or to C or to all three.

We write A ∪ B ∪ C

Basically, nosotros find A ∪ B ∪ C by putting all the elements of A, B, and C together.

A = { 1, ii, four, 6}, B = { a, b, c,} and C = A = {#, %, &,

* , $ }

A ∪ B ∪ C = { one, 2, four, 6, a, b, c,#, %, &,

* , $ }

The first graph in the outset of this lesson shows the shaded region for the wedlock of two sets.

The graph beneath shows the shaded region for the union of three sets

Union of 3 sets

This ends the lesson nearly union of sets. If you lot have any questions about the spousal relationship of sets, I will be more than happy to reply them.

Utilise the quiz below to see how well you can observe the matrimony of sets