Converse/Conditional
What is the definition of converse?
conclusion then hypothesis (q then p)
exchange hypothesis and conclusion
What is an inverse statement?
Negation (or reverse) of conditional (~p then ~q)
Make it negative!
What is a conjecture?
A prediction made/ Conclusion made
What is deductive reasoning?
A process of reasoning logically from given facts to a conclusion.
What is a hypothesis?
The part that follows "if" in an "if then" statement. (p)
What is the definition of conditional?
If then statement; Hypothesis then conclusion (p then q)
What is a contrapositive statement?
Negation of converse (~q then ~p)
Flipped and make it negative.
What is a counterexample?
An example showing that a statement is false
If the hypothesis of a true conditional is true, then the conclusion is true.
(if p then q is true and p is true... q is true)
The part that follows the "then" in an "if then" statement. (q)
What is the converse of this conditional statement...
If the figure is a square, then the figure is a quadrilateral.
If the figure is a quadrilateral, then the figure is a square.
What is the inverse of this conditional statement?
If the measure of angle A is 15 degrees, then angle A is acute
If the measure of angle A is not 15 degrees, then angle A is not acute
A sequence of numbers are given;
1, 2, 3, 5, 8,
What is the next number? Or what is the pattern?
13 or add the two previous numbers
What is the law of syllogism?
If p then q is true and q then r is true, then p then r is true.
Rewrite this statement as a conditional statement.
On Fridays students have a quiz.
If it is Friday, then the students have a quiz.
Is this a conditional statement?
Since there are 10 dogs, they are all male dogs.
No because it is not an "If then" statement
What is the contrapositive of this conditional statement?
If the measure of angle A is 15 degrees, then angle A is acute
If a shape has four equal sides it is a square. Provide a counterexample.
Rhombus
What do you conclude about these statements using the law of syllogism...
If it is December 28th, then it is winter break.
If it is winter break, then you go skiing.
If it is December 28th, then you are skiing.
Which part of this conditional statement is the hypothesis?
If it is Tuesday, then you have to walk the dog.
It is Tuesday
What does negation mean and what is its symbol?
Symbol: ~
Means "not"
What is the contrapostive of this statement?
If I turn in all my work, then I will have a good grade.
If I do not have a good grade, then I did not turn in all my work.
Does this counterexample disprove the conjecture?
Conjecture: All prime numbers are odd.
Counterexample: 7 is a prime number
No.
What can you conclude about these statements...
If it is Wednesday, then you have a tutoring session.
If you have a tutoring session, then you cannot watch tv.
If it is Wednesday, then you cannot watch tv.
What part of this conditional statement is the conclusion?
If you don't do your math homework, then you will get a bad grade in math class.
You will get a bad grade in math class.