Inv / conv / contr
If x=3 then X+1 = 4
Write the converse
If x+1=4 then x = 3
the arrow in the statement
p -> q represents
then
What law?
P -> Q
P
Law of Detachment
Use soccer/football/baseball venn diagram from packet
How many people play football and baseball
8+22=30
What are the key words for the conclusion
only if
then
implies
If she is late then she does not get to start on the team.
Write the inverse
If she is not late then she does get to start on the team
This represents the ____ of the original conditional statement q -> p
(inverse/converse/contrapositive)
Converse
What law? What is the conclusion
P ->~Q
R->P
therefore
Law of Syllogism
therefore R->~Q
Use soccer/football/baseball venn diagram from packet
How many people play soccer and football, but not baseball
15
What is the hypothesis?
MHS wins if they stay strong all game
They stay strong all game
Write the contrapositive
If it doesn't rain then they will practice
If they don't practice then it did rain
p: It is sunny
q: I am not sad
translate: ~p -> ~ q
If it is not sunny then I am sad
Is this valid? If so what law, and write the conclusion
If it is Tuesday then tomorrow is Wednesday
The 8th is Tuesday
Therefore....
Yes
Detachment
the next day (9th) is Wednesday
Use soccer/football/baseball venn diagram from packet
How many people play soccer or baseball?
23+15+8+6+22+46=120
If you go to your friends house then you get in the car
Provide a counterexample
You go to your friends house but don't get in the car, you walk
If the cat purrs then it is not full
If the cat is full it will not purr
The second sentence is the _____
contrapositive
p: x+1 = 3
q: y = 4
translate p v ~q
x+1 = 3 or y does not =4
Is this valid? If so what law, and write hte conclusion,
If she is happy then she runs
If she is happy then she smiles
therefore...
Invalid
Draw a venn diagram representing
10 people were polled, 4 like chocolate, 5 like vanilla, and 3 like both
Ask Mrs Fleck to check
All dogs have 4 legs
Rewrite the statement in if...then form
If it is a dog, then it has 4 legs
~L -> M
Write the inverse
L->~M
A single true statement that combines a true conditional and its true converse. Uses the phrase, “if and only if.”
Biconditional
Is this valid? IF so what law, and write the conclusion
If you want to buy the school lunch today, then you will need $2.50. You brought $2.50 to school today....therefore
InValid
Draw a venn diagram to represent the situation, then answer
in a survey 12 people like dogs, 7 people like cats, 3 people like both and 4 people like neither.
How many people were surveyed?
Ask Mrs Fleck to check your diagram
20 people
Calculate the distance from
A (-3,5) to B(2, 1)
Sqrt 41 or about 6.4