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Conjectures and Counterexamples (Grade 10)

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Conjectures and Counterexamples

1. 
A concluding statement reached using inductive reasoning is called a
  1. compound statement
  2. conjecture
  3. condition
  4. counterexample
2. 
Conjectures, like theorems, have been proven to be true.
  1. True
  2. False
3. 
For any right triangle, the sum of the squares of the legs is equal to the square of the hypothesis. This is an example of a conjecture.
  1. True
  2. False
4. 
No number of examples or cases can fully prove a conjecture.
  1. True
  2. False
5. 
A counterexample is an example that proves a conjecture to be true.
  1. True
  2. False
6. 
To fully disprove a conjecture, one needs to find only ONE counterexample.
  1. True
  2. False
7. 
Which of the following is a counterexample to the following conjecture? If [math]x^2=4[/math], then [math]x=2[/math]
  1. x = 4
  2. x = -2
  3. x = 2
  4. x = -4
8. 
Which number is a counterexample for the following statement?
For all numbers a, 2a + 5 < 17.
  1. a = 6
  2. a = 0
  3. a = 5
  4. a = 1
9. 
Which numbers are not counterexamples for the following statement?
For any numbers a and b, a/b = a - b
  1. a = 8, b = 4
  2. a = 10, b = 5
  3. a = 6, b = 3
  4. a = 4, b = 2
10. 
Which answer would be a counterexample to the biconditional, "Greg is a swimmer if and only if he is an athlete."
  1. Greg is an athlete and a basketball player.
  2. Greg is a swimmer.
  3. Greg is not an athlete.
  4. There is no counterexample.
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