Monday, February 2, 2009

Sets

Read over the chapter on sets in Book 1. It gives a good overview and covers all of the notation well. There is a little bit of higher level work on maximising and minimising sets which is very simple, but we'll do it after the mocks.
For now, make sure that you know all the notation and that you know how to deal with unknowns using a Venn diagram.
Don't forget that you fill a Venn diagram from the centre outwards.
For question 4:
Draw two circles marked A and B with a decent overlap.
The overlap area represents A ∩ B and the number of elements in the area is 6.
That means that the shape representing A not B or A\B is going to contain the number 13-6=7 and the 3rd region represented by B\A will contain the number 14-6= 8.
So reading left to right (assuming you've laid your work out that way with A on the left and B of the right) you will have the numbers 7 then 6 then 8.
That means that the total number of elements in A∪B is 7+6+8=21.
The total number of elements in A∪B is written as #(A∪B).


General point:
If you have numbers with dots beside them in a region of a Venn diagram then those numbers are the elements of a set.
If you have a single number and no dot beside it, then that number is the number of elements in that region.

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