AND OR AND OR AND OR AND OR OR AND AND OR AND OR NOT NOT What do these words mean MATHEMATICALLY???

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Presentation transcript:

AND OR AND OR AND OR AND OR OR AND AND OR AND OR NOT NOT What do these words mean MATHEMATICALLY???

What is a statement? Statement is a sentence that is either true or false. So….Which remark(s) are statements? -Eggs give you protein -Eggs do not give you protein -Eggs is the best thing for breakfast Compound Statement: A statement formed by connecting one or more statements with as, or, not, and Ex. Joe is sixteen (what is this?) Joe has blue eyes(what is this?) Joe is sixteen and has blue eyes(what is this and what does it mean?) Negation: NOT Joe is not sixteen Joe does not have blue eyes Joe is not sixteen and does not have blue eyes

AND -Is inclusive (tells which group or condition it belongs to -Means both conditions apply (are TRUE) Ex. To be in the Miss Canada Pageant, you must be a girl AND over is a integer AND it is greater than 0

OR -Is inclusive (tells which group or condition it belongs to) -Means at least one of the conditions are true, But also when both conditions are true Ex. Nick only dates girls who are smart OR rich Solution is: Could be smart, but not rich Could be rich but not smart Could be rich and smart

Which values of x make the following true? x is a factor of 12 AND x is a factor of 28 Solution: x is a factor of 12 AND x is a factor of 28 1,2,3,4,6,121,2,4,7,14,28 what is common in both: 1,2,4 x is a factor of 12 OR x is a factor of 28 Solution: x is a factor of 12 OR x is a factor of 28 1,2,3,4,6,7,12,14,28 these answers with OR means that they show up on at least one of the lists (but could be on BOTH lists)

Venn Diagrams

Last example: Nick likes girls that are smart OR rich

Venn Diagram The following example using sports Running, Swimmer, Biking How many do all 3 sports? How many only do each one? How many run and bike? How many bike and swim? How many run but do not swim? How many don’t do anything? How many kids are there in total?

Do the following example Ex. Grade 11 students 380 took Bio 240 took Chem 150 took physics 125 took all took none 140 took physics and chem 220 took bio and chem 130 took bio and physics How many took only bio? How many students ?

Hints about Venn Diagrams Start in the middle Then do other overlaps Read carefully

Number lines