Rajesh told Shyam that he did not like this party change into direct speech
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SETS AND VENN DIAGRAMS
Number and Algebra : Module 1Years : 7-8
June 2011
PDF Version of module
Assumed knowledge
Motivation
Content
Describing and naming sets
Subsets and Venn diagrams
Complements, intersections and unions
Solving problems using a Venn diagram
Links Forward
Sets and probability
History and applications
Answers to Exercises
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ASSUMED KNOWLEDGE
Addition and subtraction of whole numbers.
Familiarity with the English words
‘and’, ‘or’, ‘not’, ‘all’, ‘if…then’.
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MOTIVATION
In all sorts of situations we classify objects into sets of similar objects and count them. This procedure is the most basic motivation for learning the whole numbers and learning how to add and subtract them.
Such counting quickly throws up situations that may at first seem contradictory.
‘Last June, there were 15 windy days and 20 rainy days, yet 5 days were neither windy nor rainy.’
How can this be, when June only has 30 days? A Venn diagram, and the language of sets, easily sorts this out.
Let W be the set of windy days,
and R be the set of rainy days.
Let E be the set of days in June.
Then W and R; together have size 25, so
the overlap between W and R is 10.; The Venn diagram opposite displays; the whole situation.
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