
Understanding Proof by Counterexample

Interactive Video
•
Mathematics
•
9th - 12th Grade
•
Hard
Standards-aligned

Emma Peterson
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main topic introduced in the beginning of the video?
Proof by induction
Proof by contradiction
Proof by construction
Proof by counterexample
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the converse of the statement 'If a + b is odd, then a is odd or b is odd'?
If a + b is odd, then a is even or b is even
If a + b is even, then a is even or b is even
If a is odd or b is odd, then a + b is odd
If a is even or b is even, then a + b is even
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the converse statement considered false?
Because it contradicts the original statement
Because it cannot be proven
Because there exists a counterexample
Because it is logically equivalent to the original statement
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the logical equivalent of negating the implication 'If p then q'?
not p or q
p and not q
not p and q
p or not q
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the negation of the converse statement imply?
There are no integers a and b such that a is odd or b is odd and a + b is odd
There exists integers a and b such that a is odd or b is odd and a + b is not odd
All integers a and b are even
All integers a and b are odd
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which integers are used as a counterexample to prove the negation of the converse?
a = 2, b = 4
a = 0, b = 2
a = 1, b = 3
a = 3, b = 5
Tags
CCSS.3.OA.D.9
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the sum of the integers used in the counterexample?
3
5
4
2
Tags
CCSS.3.OA.D.9
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