Drawing Conclusions
Conditional Statements
Converse
(switch)
(switch)
Inverse
(negate)
(negate)
Contrapositive
(switch/negate)
(switch/negate)
100
Subway: "Eat Fresh"
What conclusion can you draw about the type of food this company sells?
The food is fresh.
100
If it rains, then the ground gets wet.
What is the hypothesis?
If it rains.
100
What is the converse(switch)?
If it rains, then the ground gets wet.
If the ground is wet, then it rains.
100
What is the inverse(negate)?
If it rains, then the ground gets wet.
If it doesn't rain, then the ground is not wet.
100
What is the contrapositive(switch/negate)?
If it rains, then the ground gets wet.
If the ground is not wet, then it didn't rain.
200
What conclusion can you draw about the temperature outside?
It was cold outside.
200
If Mr. Sousa only has a mustache, then it is the month of November.
What is the conclusion?
It is the month of November.
200
What is the converse?
If you get a 60 on the test, then you failed.
If you failed, then you got a 60 on the test.
200
What is the inverse?
If you get a 60 on the test, then you failed.
If you did not get a 60 on the test, then you did not fail.
200
What is the contrapositive?
If you get a 60 on the test, then you failed.
If you didn't fail, then you didn't get a 60 on the test.
300
A student's paper has lots of eraser marks and crossed-out work.
What conclusion can you draw about how they approached the assignment?
They were checking and revising their work or made mistakes they corrected.
300
When a statement is written in "if-then" form, what is it called?
Conditional Statement
300
In terms of the symbolism a → b, how do we write a converse(switch) of a statement?
b → a
300
In terms of the symbolism a → b, how do we write a inverse(negate) of a statement?
not a → not b
300
In terms of the symbolism a → b, how do we write a Contrapositive(switch/negate) of a statement?
not b → not a
400
What conclusion can you draw about what recently happened in the hallway?
The floor was just cleaned or something spilled.
400
Write in "if-then" form.
No calculators are edible.
If it is a calculator, then it is not edible.
400
Is the converse of a statement always true?(if not, give a counter example)
No, "if you failed, then you got a 60 on the test", you could fail with a 55 or other scores.
400
Is the inverse of a statement always true?(if not, give a counter example)
No, "If you did not get a 60 on the test, then you didn't fail" is not true, I could have failed with a 55.
400
Is the contrapositive of a conditional statement always true?(if not, give a counter example)
Yes it is!
500
Slogan: "Red Bull gives you wings"
What conclusion can you draw about how the company wants customers to feel after drinking it?
Energized, able to do more than normal, like they have extra power.
500
Write in "if-then" form:
I will make a birdie when I finally drive the green.
If I finally drive the green, then I will make a birdie.
500
What is the converse, is it true?
If you live in Maine, then you live in the U.S.
If you live in the U.S., then you live in Maine. That is false.
500
What is the inverse, is it true?
If a number is even, then it is divisible by 2.
If a number is not even, then it is not divisible by 2, true!
500
What is the contrapositive, is it true?
If you live in Maine, then you live in the U.S.
If you do not live in the U.S., then you do not live in Maine, true!