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WorksheetsMastering Math Deductive Proofs
Total questions: 20
Worksheet time: 10mins
What is a logical fallacy? Provide an example.
A logical fallacy is a valid reasoning process that leads to a correct conclusion.
An example of a logical fallacy is the 'ad hominem' fallacy, where someone attacks the character of the person making an argument rather than addressing the argument itself.
An example of a logical fallacy is the 'straw man' fallacy, where one misrepresents an argument to make it easier to attack.
A logical fallacy is a type of argument that is always true.
Identify the fallacy in the statement: 'If it rains, the ground is wet. The ground is not wet, therefore it did not rain.'
Affirming the consequent
Straw man argument
Circular reasoning
Denying the antecedent
Construct a direct proof to show that if n is an even integer, then n^2 is also even.
If n is an even integer, then n^2 is also even.
If n is an odd integer, then n^2 is also odd.
If n is an even integer, then n^2 is odd.
If n is an even integer, then n^2 is a prime number.
Use an indirect proof to show that the square root of 2 is irrational.
The square root of 2 is rational.
The square root of 2 is irrational.
The square root of 2 is a whole number.
The square root of 2 can be expressed as a fraction.
Apply the transitive property of equality to prove: If a = b and b = c, then a = c.
c = b
a = c
a = b
b = a
What is the definition of the reflexive property of equality?
For any value a, a + b = a.
For any value a, a = b.
For any value a, a ≠ a.
For any value a, a = a.
Analyze the following proof: 'If a = b, then a + c = b + c. Therefore, if a + c = d, then b + c = d.' Is it valid? Why or why not?
No, the conclusion does not logically follow from the premises.
No, the proof is invalid because it assumes a = b without justification.
Yes, the proof is valid.
Yes, but only if c = 0 for the proof to hold.
Construct a direct proof to show that the sum of two odd integers is even.
The sum of two odd integers is prime.
The sum of two odd integers is even.
The sum of two odd integers is zero.
The sum of two odd integers is odd.
Use properties of equality to solve for x: 3x + 5 = 20.
10
15
0
5
Identify the logical fallacy in the argument: 'Everyone who eats vegetables is healthy. John eats vegetables, so he is healthy.'
Straw man
Hasty generalization
False dilemma
Ad hominem
What is the difference between a direct proof and an indirect proof?
A direct proof relies on assumptions, while an indirect proof uses examples.
A direct proof is longer and more complex than an indirect proof.
A direct proof uses straightforward logic, while an indirect proof assumes the opposite and derives a contradiction.
A direct proof can only be used for numerical problems, while an indirect proof is for logical statements.
Analyze this geometric proof: 'In triangle ABC, if angle A is greater than angle B, then side a is greater than side b.' Is it valid?
No, the proof is invalid.
Yes, the proof is valid.
Angle A and angle B cannot be compared.
The proof is only valid for right triangles.
Construct a direct proof to show that the product of two even numbers is even.
The product of two odd numbers is even.
The product of two even numbers is even.
The product of an even and an odd number is odd.
The product of two even numbers is odd.
Use an indirect proof to show that if x^2 is even, then x must be even.
x is always negative.
x must be a prime number.
x can be odd.
x must be even.
Apply the substitution property of equality to prove: If a = 2 and b = a + 3, what is b?
6
4
5
7
Identify the fallacy in the statement: 'If I study hard, I will pass. I did not pass, therefore I did not study hard.'
Affirming the consequent fallacy
Straw man fallacy
Circular reasoning fallacy
Denying the antecedent fallacy
What is the significance of the symmetric property of equality?
It ensures that if a = b, then b = a, facilitating logical reasoning and equation manipulation.
It allows for the conclusion that a = a is false.
It states that if a = b, then a + c = b + c.
It implies that a and b must be different values.
Construct a direct proof to show that the difference of two even integers is even.
The difference of two even integers is even.
The difference of two odd integers is even.
The product of two even integers is odd.
The sum of two even integers is even.
Use properties of equality to prove: If x + 4 = 10, then x = 6.
x = 4
x = 2
x = 6
x = 10
Analyze the following geometric proof: 'If two angles are supplementary, then their measures add up to 180 degrees.' Is it valid?
The proof is valid only for right angles.
Yes, the proof is valid.
Supplementary angles always add up to 360 degrees.
The proof is invalid because angles can be any measure.
