Conditional Statements Review

Conditional Statements Review

What is a conjecture?

an opinion or conclusion formed on the basis of incomplete information.

What is a counterexample?

Example: All animals have fur.

Counterexample: Fish (fish does not have fur)

Multiple Choice

True or False: a counterexample is an example that makes a definition or conjecture incorrect

• True
• False

Multiple Choice

If an animal is furry, then it is a hamster. What would be an appropriate counterexample?

• goldfish
• frog
• elephant
• cat

Multiple Choice

If something is an angle, then it is acute. What is an appropriate counterexample?

• 70⁰
• 45⁰
• 120⁰
• True. There is no counterexample.

Multiple Choice

If something is a vehicle, then it is a Hyundai. What is an appropriate counterexample?

• Hyundai Sonata

• Mercedes Benz

• Hyundai Genesis

• Both A and C are counterexamples.

Logic Statement _{Hypothesis p Conclusion q}

• Conditional p→q If you are an artist, then you draw well

• Inverse ~p→~q If you are not an artist, then you do not draw well

• Converse q→p If you draw well, then you are an artist

• Contrapositive ~q→~p If you do not draw well, then you are not an artist

• Biconditional p↔q You are an artist IF AND ONLY IF you draw well

Biconditional statement

Usually is a definition since both ways are true

Example:

If a polygon is a triangle, it has three sides.

If a polygon has three sides, it is a triangle.

Biconditional: A polygon is a triangle if and only if it has three sides.

Multiple Choice

The statement "an angle is a right angle if and only if its measure is 90^o" is an example of what type of statement?

• Conditional

• Conjecture

• Biconditional

Multiple Choice

This symbol, ↔, means?

• and
• or 
• if and only if
• implies

Multiple Select

What are the two parts of a conditional statement?

• Hypothesis

• Conclusion

• Converse

• Inverse

Multiple Choice

What is it hypothesis in the statement:" If today is Tuesday, then we have school."?

• Tomorrow is Wednesday.

• We have school.

• Today is Tuesday.

• We do not have school.

Multiple Choice

Write the conclusion of the statement,

"If you are Anthony Rizzo, then you are a Chicago Cub."

• You are Anthony Rizzo.

• You are a Chicago Cub.

• The Cubs are the best.

Multiple Choice

Identify the hypothesis and conclusion of the conditional statement:
If you give me twenty dollars, then I will be your best friend.

• Hypothesis: I will be your best friend
  Conclusion: you give me twenty dollars
• Hypothesis: you give me twenty dollars
  Conclusion: I will be your best friend
• Hypothesis: if you have to pay for friends
  Conclusion: then you probably should reevaluate your life
• Hypothesis: you will not have to pay twenty dollars
  Conclusion: if you have lots of friends

Multiple Choice

What is this?

• Conditional Statement
• Inverse
• Converse
• THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS!

Multiple Choice

p→q
What is the converse?

• q→p
• ∼p→∼q
• ∼q→∼p
• p→∼q

Multiple Choice

What does this mean?

• Conditional Statement
• Inverse Statement
• Converse Statement
• Contrapositive Statement

Multiple Choice

What is this mean?

• Conditional Statement
• Converse
• Inverse
• Contrapositive

Multiple Choice

Write the inverse of the following statement.

"If a figure is a triangle, then the angles add to 180.

• If a figure is not a triangle, then the angles do not add to 180.

• If the angles of a figure do not add to 180, then it is not a triangle.

• If a figure has angles that add to 180, then it is a triangle.

Multiple Choice

Write the inverse of
 $If\ 3x\ =\ 15,\ then\ x\ =\ 5.\$  

•  $If\ x\ \ne5,\ then\ 3x\ \ne15.$ 

•  $If\ x\ =\ 5,\ then\ 2x\ =\ 10.$  

•  $If\ \ 3x\ \ne15,\ then\ x\ne5.$ 

•  $If\ x\ =\ 5,\ then\ 3x\ =\ 15.\$  

Multiple Choice

Write the converse of
 $If\ 3x\ =\ 15,\ then\ x\ =\ 5.\$  

•  $If\ x\ \ne5,\ then\ 3x\ \ne15.$ 

•  $If\ x\ =\ 5,\ then\ 2x\ =\ 10.$  

•  $If\ \ 3x\ \ne15,\ then\ x\ne5.$ 

•  $If\ x\ =\ 5,\ then\ 3x\ =\ 15.\$  

Multiple Choice

Write the contrapositive of the following statement.

"If a figure is a triangle, then the angles add to 180.

• If a figure is not a triangle, then the angles do not add to 180.

• If the angles of a figure do not add to 180, then it is not a triangle.

• If a figure has angles that add to 180, then it is a triangle.

Multiple Choice

Original: If Jenny buys a guitar, then she will not buy a keyboard.
What is this? If Jenny does buy a keyboard, then she will not buy a guitar.

• Converse
• Inverse
• Contrapositive
• Negation

Multiple Choice

Write the contrapositive of
 $If\ 3x\ =\ 15,\ then\ x\ =\ 5.\$  

•  $If\ x\ \ne5,\ then\ 3x\ \ne15.$ 

•  $If\ x\ =\ 5,\ then\ 2x\ =\ 10.$  

•  $If\ \ 3x\ \ne15,\ then\ x\ne5.$ 

•  $If\ x\ =\ 5,\ then\ 3x\ =\ 15.\$  

Multiple Choice

Write the converse of the following statement.

"If a figure is a triangle, then the angles add to 180.

• If a figure is not a triangle, then the angles do not add to 180.

• If the angles of a figure do not add to 180, then it is not a triangle.

• If a figure has angles that add to 180, then it is a triangle.

Multiple Choice

Which is the correct if-then statement for: "you will be late to school if you miss the bus."

• If you are late to school, then you will miss the bus.
• If you miss the bus, then you will be late to school
• If you sleep late, then you don't have to go to school.
• If you miss the bus, then you'll have to walk and be late.

Multiple Choice

Rewrite the statement as a conditional statement.

"All dolphins are mammals."

• If a dolphin, then a mammal.

• If an animal is a dolphin, then it is a mammal.

• If an animal is a mammal, then it is a dolphin.

• If an animal is not a mammal, then it is not a dolphin.

Multiple Choice

Rewrite the statement as a conditional statement.

"The sum of the angles of a triangle is 180."

• If the sum of the angles of a triangle, then 180.

• If a figure is a triangle, then the sum of the angles is 180.

• If a figure sums angles, then the triangle is 180.

Multiple Choice

Write the following statement in if-then form.
All students at Hermitage take an English class.

• If you take an English class, then you are a student at Hermitage.
• If you are a student at Hermitage, then you take an English. class