Union And Intersection Venn Diagram

Sets and Venn Diagrams

Sets

A fix is a collection of things.

For instance, the items you lot article of clothing is a fix: these include hat, shirt, jacket, pants, and so on.

Yous write sets inside curly brackets similar this:

{hat, shirt, jacket, pants, ...}

You can also have sets of numbers:

• Set of whole numbers: {0, 1, 2, 3, ...}
• Set of prime number numbers: {2, 3, 5, 7, 11, 13, 17, ...}

X Best Friends

You lot could accept a set fabricated up of your ten all-time friends:

• {alex, blair, casey, drew, erin, francis, glen, hunter, ira, jade}

Each friend is an "element" (or "member") of the prepare. It is normal to employ lowercase letters for them.

Now allow's say that alex, casey, drew and hunter play Soccer:

Soccer = {alex, casey, drew, hunter}

(It says the Gear up "Soccer" is made upward of the elements alex, casey, drew and hunter.)

And casey, drew and jade play Tennis:

Tennis = {casey, drew, jade}

We can put their names in two separate circles:

Wedlock

You can at present listing your friends that play Soccer OR Lawn tennis.

This is called a "Union" of sets and has the special symbol ∪:

Soccer ∪ Tennis = {alex, casey, drew, hunter, jade}

Non everyone is in that set ... only your friends that play Soccer or Lawn tennis (or both).

In other words nosotros combine the elements of the 2 sets.

Nosotros can show that in a "Venn Diagram":

Venn Diagram: Union of two Sets

A Venn Diagram is clever because it shows lots of information:

• Practise yous see that alex, casey, drew and hunter are in the "Soccer" set?
• And that casey, drew and jade are in the "Tennis" set?
• And here is the clever affair: casey and drew are in BOTH sets!

All that in one minor diagram.

Intersection

"Intersection" is when y'all must exist in BOTH sets.

In our case that ways they play both Soccer AND Tennis ... which is casey and drew.

The special symbol for Intersection is an upside down "U" like this: ∩

And this is how we write information technology:

Soccer ∩ Lawn tennis = {casey, drew}

In a Venn Diagram:

Venn Diagram: Intersection of 2 Sets

Which Way Does That "U" Go?

Call back of them every bit "cups": ∪ holds more h2o than ∩, right?

So Union ∪ is the one with more elements than Intersection ∩

Difference

Y'all tin can also "subtract" i set from some other.

For instance, taking Soccer and subtracting Tennis means people that play Soccer but NOT Tennis ... which is alex and hunter.

And this is how we write information technology:

Soccer − Tennis = {alex, hunter}

In a Venn Diagram:

Venn Diagram: Difference of 2 Sets

Summary Then Far

• ∪ is Union: is in either set up or both sets
• ∩ is Intersection: merely in both sets
• − is Difference: in one set but not the other

Iii Sets

You tin can also use Venn Diagrams for three sets.

Let u.s. say the 3rd set is "Volleyball", which drew, glen and jade play:

Volleyball = {drew, glen, jade}

But let'due south be more "mathematical" and utilise a Capital Letter for each set up:

• S means the ready of Soccer players
• T means the prepare of Tennis players
• V means the set of Volleyball players

The Venn Diagram is now like this:

Wedlock of three Sets: Southward ∪ T ∪ Five

You lot can run into (for case) that:

• drew plays Soccer, Tennis and Volleyball
• jade plays Tennis and Volleyball
• alex and hunter play Soccer, merely don't play Tennis or Volleyball
• no-one plays just Tennis

We can at present have some fun with Unions and Intersections ...

This is just the set up South

South = {alex, casey, drew, hunter}

This is the Union of Sets T and V

T ∪ Five = {casey, drew, jade, glen}

This is the Intersection of Sets South and Five

S ∩ V = {drew}

And how well-nigh this ...

• take the previous set South ∩ V
• then subtract T:

This is the Intersection of Sets South and V minus Ready T

(Southward ∩ V) − T = {}

Hey, at that place is nothing there!

That is OK, information technology is just the "Empty Set". It is still a gear up, so nosotros utilize the curly brackets with nothing inside: {}

The Empty Set has no elements: {}

Universal Set up

The Universal Set is the ready that has everything. Well, not exactly everything. Everything that we are interested in now.

Sadly, the symbol is the alphabetic character "U" ... which is easy to confuse with the ∪ for Union. Y'all just have to be careful, OK?

In our case the Universal Set up is our Ten All-time Friends.

U = {alex, blair, casey, drew, erin, francis, glen, hunter, ira, jade}

We can testify the Universal Set in a Venn Diagram past putting a box around the whole thing:

Now you tin can see ALL your ten best friends, neatly sorted into what sport they play (or not!).

Then nosotros can do interesting things like accept the whole set up and subtract the ones who play Soccer:

We write it this way:

U − S = {blair, erin, francis, glen, ira, jade}

Which says "The Universal Set minus the Soccer Set is the Set {blair, erin, francis, glen, ira, jade}"

In other words "everyone who does not play Soccer".

Complement

And there is a special way of proverb "everything that is not", and information technology is called "complement" .

We prove it by writing a little "C" like this:

S^c

Which means "everything that is NOT in Southward", like this:

S^c = {blair, erin, francis, glen, ira, jade}
(exactly the same as the U − South example from above)

Summary

• ∪ is Marriage: is in either fix or both sets
• ∩ is Intersection: only in both sets
• − is Difference: in one set but not the other
• A^c is the Complement of A: everything that is not in A
• Empty Set: the set up with no elements. Shown by {}
• Universal Prepare: all things we are interested in

1886, 1887, 1890, 1892, 7220, 1888, 1889, 1891, 91, 73

Union And Intersection Venn Diagram,

Source: https://www.mathsisfun.com/sets/venn-diagrams.html

Posted by: marcellosalict67.blogspot.com

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