Sets Done by : Mohamed Nasser Dayan 9ASP - 2
What is a set ? A set is a collection of things. For example, the items you wear is a set: these would include shoes, socks, hat, shirt, pants, and so on. Y ou have to write sets inside curly brackets like this : ( shoes, socks, hat, shirt, pants.... ) . Y ou can also have sets of numbers: Whole numbers: ( 0,1,2,3... ) Prime numbers: ( 2,3,5,7... )
Six Volunteers Y ou could have a set made up of six volunteers : ( Salem,Mohamed,Sultan, Abdullah,Ahmed,Ayman ) . Each volunteer is an "element" ( or"member" ) . Now let's say that Salem and Mohamed will donate blood.Donate blood : ( Salem,Mohamed ) . The set of donating blood is made up of elements Salem,Mohamed. And Abdullah and Ayman will serve breakfast. ( Abdullah,Ayman ) . Y ou could put their names in two separate circles: Donate blood Serve breakfast Salem,Mohamed Abdullah,Ayman
Intersection "Intersection" is when you have to be in BOTH sets or the common between the sets or the overlapping in the venn diagram. In our case it means they will donate blood and serve breakfast. Which is Sultan and Ahmed. The special symbol for intersection is upside down a U like this : ∩ . And it's written like this : donate blood ∩ serve break fast : ( sultan , ahmed ) donate blood serve breakfast sultan, ahmed
Union The union of two sets is the set of all elements from sets A, B, or both. In our case it means that all of the volunteers. It's symbol is an U. It's written like this : serve break fast U donate blood.
Difference Y ou can also "subtract" one set from another. For example, taking volunteers who donate blood and subtract them from volunteers who serve breakfast. Which is ( Abdullah and Ayman ) . And the symbol is - and it will be written like this : Donate blood - serve breakfast : ( Abdullah,Ayman ) . Donate blood Serve breakfast Abdullah , Ayman
Complement And there is a special way of saying "everything that is not", and it is called "complement". It's symbol is this '. For example , Serve breakfast': ( Salem , Mohamed ) . Serve Breakfast Donate blood Salem,Mohamed
Empty set This is the Intersection of Sets S and V minus Set T ( S ∩ V ) − T = {} Hey, there is nothing there! That is OK, it is just the "Empty Set". It is still a set, so we use the curly brackets with nothing inside: {}
Universal The Universal Set is the set that contains everything. Sadly, the symbol is the letter "U" ... which is easy to confuse with the ∪ for Union. Y ou just have to be careful, OK? In our case the universal : ( Salem,Mohamed,Sultan, Abdullah,Ahmed,Ayman ) . W e can show the Universal Set in a V enn Diagram by putting a box around the whole thing:
Summary ∪ is Union: is in either set ∩ is Intersection: must be in both sets − is Di ff erence: in one set but not the other Ac is the Complement of A: everything that is not in A Empty Set: the set with no elements. Shown by {} Universal Set: all things we are interested in
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