Conditional Statements
Write the statement as a conditional statement: You are tall if you are over six feet.
If you are tall, then you are over six feet.
A biconditional statement contains what phrase?
If and only if
Finish the pattern: 2, 22, 222, 2222,....
22222
Name the two laws of logic in deductive reasoning
Law of Detachment and Law of Syllogism
A conditional statement is written in if-then form. The if part contains the ________, and the then part contains the _________.
Hypothesis and Conclusion
Write the converse of the following statement: If it snows, then it is winter.
If it is winter, then it snows.
Write the negation of the following statement:I will ace this test
I will not ace this test
True or False: Inductive reasoning reasoning is used to make the conclusion.
Each time your mom goes to the store she buys milk. So, the next time your mom goes to the store, she will buy milk.
True
Deductive reasoning is based on what?
Facts, definitions, or accepted properties and the laws of logic
The _________ of a statement is the opposite of the original statement.
negation
Write the inverse of the statement: If I drink water, I won't be dehydrated.
If I don't drink water, I will be dehydrated.
What are the symbols for a biconditional statement.
p <--> q
Make a conclusion: Each time you forget to do your math homework, your grade goes down. You forget to do your math homework,.......
Your grade went down.
What law of logic is used?
If x>12, then x+9>20. The value of x is 14. So, x+9>20.
Law of Detachment
A __________ is an unproven statement based on observation.
Conjecture
Write the contrapositive of the following statement: If it is hot out, then the ice cream will melt.
If the ice cream doesn't melt, then it is not hot out.
Write as a biconditional statement: If two angles are complementary, then they add up to 90 degrees.
Two angles are complementary if and only if they add up to 90 degrees.
Use inductive reasoning to to make a conjecture about the given quantity.
The sum of two odd integers.
Always even
True or False: Deductive Reasoning is used to make a conclusion: All men are mortal. Mozart is a man, so Mozart is mortal.
True
You can show a conjecture is false by showing just one _________.
Counterexample
Write the following as its contrapositive and state whether it is true or false. If 3x-7=20, then x=9.
If x doesn't equal 9, then 3x-7 does not equal 20. True
Rewrite as a biconditional statement: Two angles are supplementary when the sum of their measure is 180
Two angles are supplementary if and only if the sum if their measures is 180
Find a counterexample: The product of two positive numbers is always greater than either number.
Anything multiplied by 1
Use law of syllogism to make a conclusion. If a figure is a rhombus, then the figure is a parallelogram. If a figure is a parallelogram, then the figure has two pairs of opposite sides that are parallel.
If a figure is a rhombus, then the figure has two pairs of of opposite sides that are parallel.
Law of __________, is if the hypothesis of a true conditional statement is true, then the conclusion is also true.
Detachment