Conditionals
Identify the hypothesis and conclusion:
If you study for your test, then you will get a good grade.
hypothesis: you study for your test
conclusion: you will get a good grade
Used to prove a conjecture false
counterexample
A type of reasoning that reaches conclusions based on a pattern
inductive reasoning
A biconditional is true if the ______ and _______ are true.
conditional and converse
Saying that a statement is true or false is called:
truth value
What do you call an "if-then" statement?
conditional statement
Prove the statement false with a counterexample:
All fractions are between 0 and 1.
possible answer: 5/4
A rule based on a pattern
conjecture
Write the biconditional:
If I spend $75 online, then I will get free shipping.
I spend $75 online if and only if I get free shipping.
What is the truth value for the conditional:
If it is below 32 degrees, then it snowed.
False
Write the converse:
If you study for your test, you will get a good grade.
Prove the statement false with a counterexample:
Every city in Alabama starts with the letter A.
possible answer: Daphne
Complete the sequence:
1,1,2,3,5,8,__,___
13,21
The converse is where you _____ the hypothesis and conclusion.
swap
What is the truth value for the CONVERSE of the statement:
If it is below 32 degrees, then it snowed.
converse: If it snowed, then it is below 32 degrees.
true
Write the inverse:
If you study for your test, then you will get a good grade.
If you did not get a good grade, then you did not study for your test.
Prove the statement false with a counterexample:
Supplementary angles are always equal.
possible answer: 150 and 30 are supplementary and not equal to each other
Complete the sequence:
-2,-4,-6,-8,__,__
-10,-12
The inverse is where you ________ the hypothesis and conclusion.
negate
What is the truth value for the INVERSE of the statement:
If it is below 32 degrees, then it snowed.
The inverse says: If it is not below 32 degrees, then it did not snow.
True
Write the contrapositive:
If you did not study for the test, then you did not get a good grade.
If you did not get a good grade, then you did not study for the test.
Prove the statement false with a counterexample:
If an angle is acute, then it is 45 degrees.
possible answer: 30 is acute
Complete the sequence:
A,C,E,__,___
G,I
The contrapositive is where you ______ and ______ the hypothesis and conclusion.
swap and negate
What is the truth value for the CONTRAPOSITIVE of the statement:
If it is below 32 degrees, then it snowed.
contrapositive: if it did not snow, then it is not below 32 degrees.
false