Common Logical Fallacies

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Show your work for each problem.

1.
Argument: If it rains, the ground is wet. The ground is wet. Therefore it rained. Which fallacy is this?
1. a)Circular reasoning
2. b)Denying the antecedent
3. c)Straw man
4. d)Affirming the consequent
2.
An ad says: 4 out of 5 users improved their grades! What percentage is 4 out of 5?
3.
Argument: If $x = 4$ , then $x^2 = 16$ . We know that $x^2 = 16$ . Therefore $x = 4$ . Find a counterexample.
4.
Maya shows that $x = 5$ solves $2x + 3 = 13$ . Leo answers: Don't listen to her, she failed the last test. Which fallacy does Leo use?
1. a)Slippery slope
2. b)False dilemma
3. c)Appeal to authority
4. d)Ad hominem
5.
After checking 3, 5 and 7, Tom claims: every odd number greater than 1 is prime. What is the smallest odd number greater than 1 that proves him wrong?
6.
Argument: Every integer is either positive or negative. Find the option this false dilemma leaves out.
7.
Ana: We should check our answer with a second method. Ben: So you think we can never trust any calculation? That's ridiculous. Which fallacy does Ben use?
1. a)Appeal to authority
2. b)Straw man
3. c)Denying the antecedent
4. d)Hasty generalization
8.
A school has 500 students and 450 of them use the app StudyFast. 60 students got an A in math, and 54 of them use the app. An ad says: 90% of A students use StudyFast, so the app causes A grades! What percentage of the app users got an A?
9.
Argument: If a number is a multiple of 10, then it is a multiple of 5. 15 is not a multiple of 10. Therefore 15 is not a multiple of 5. Show that the argument fails.
10.
Claim: This formula is correct because it always gives the right answers, and we know the answers are right because they come from this formula. Which fallacy is this?
1. a)Correlation vs causation
2. b)Circular reasoning
3. c)Ad hominem
4. d)Slippery slope
11.
Rule: If a number is divisible by 6, then it is even. Someone affirms the consequent and treats every even number as divisible by 6. How many even numbers from 1 to 20 are counterexamples (even but not divisible by 6)?
12.
In a class of 40, 25 students play an instrument and 20 of them have a math grade above 80. Of the 15 who don't play, 6 have a grade above 80. Claim: playing an instrument makes you better at math. Compare the two groups.
13.
A slippery slope: If you skip one homework, you will fall behind, then fail the next test, then fail the whole year. Suppose each of these three steps really happens with probability $0.5$ , independently. What is the chance that all three happen, as a percentage?
14.
Argument: If a number ends in 0, then it is divisible by 5. 35 is divisible by 5. Therefore 35 ends in 0. Check the argument.
15.
Argument: If a number is divisible by 9, then it is divisible by 3. 21 is not divisible by 9. Therefore 21 is not divisible by 3. Which statement is correct?
1. a)The argument affirms the consequent, but its conclusion is true
2. b)The argument is valid, because 21 is not divisible by 9
3. c)The argument is valid, because it is modus tollens
4. d)The argument denies the antecedent, and 21 is a counterexample because $21 \div 3 = 7$
16.
A student checks $n^2 - n + 11$ for $n = 1$ to $10$ and gets only primes: 11, 13, 17, 23, 31, 41, 53, 67, 83, 101. She claims the result is always prime. What is the value of $n^2 - n + 11$ for $n = 11$ ?
17.
A headline says: Risk doubles! A side effect rises from 1 in 10000 people to 2 in 10000 people. Find out how big the change really is.
18.
A disease affects 20 of 1000 people. A test is positive for 18 of the 20 sick people, and by mistake also for 42 of the 980 healthy people. Claim: the test finds 90% of sick people, so a positive result means a 90% chance of being sick. What is the real chance, as a percentage?