Deductive Reasoning

Which of the following is a counterexample:

If a boy is tall, then he is good at basketball

• Lebron is tall and good at basketball

• Jerry is short and good at basketball

• Frank is tall and bad at basketball

• Harry is short and bad at basketball

If it is a line, then it has a positive slope. What is an appropriate counterexample?

• y = -4x
• y = 6x
• y = 1/5x + 5
• y = 2x - 6

Tags

CCSS.8.EE.B.5

If it is a fraction, then it is a number between zero and one. What is an appropriate counterexample?

• 2/3
• 4/5
• 1/2
• 3/2

Tags

CCSS.6.NS.C.7A

CCSS.6.NS.C.7B

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

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

Tags

CCSS.7.G.B.5

If it is a number, then it is either positive or negative. What is an appropriate counterexample?

• 10
• -2
• 0
• True. There is no counterexample.

Tags

CCSS.6.NS.C.5

If a shape is round, then it is a circle. What is an appropriate counterexample?

• hexagon
• oval
• triangle
• square

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

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

• True
• False

Tags

CCSS.HSG.CO.C.11

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

When taking the converse of a statement we_____ the hypothesis and the conclusion.

• negate
• highlight
• switch
• switch and negate

Given: If I have a Siberian Husky, then I have a dog
Identify the contrapositive

• If I do not have a Siberian Husky, then I do not have a dog
• If I do not have a dog, then I do not have a Siberian Husky.
• If I have a dog, then I have a Siberian Husky
• If I have a dog, then I don't have a Siberian Husky