Introduction to Logical Reasoning

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Show your work for each problem.

1.
Which type of reasoning starts with specific observations and forms a general conclusion?
1. a)Inductive reasoning
2. b)Circular reasoning
3. c)Random reasoning
4. d)Deductive reasoning
2.
In an argument, what are statements assumed to be true called?
1. a)Premises
2. b)Conclusions
3. c)Theories
4. d)Hypotheses
3.
Premise 1: Every spider has exactly 8 legs. Premise 2: There are 3 spiders in a box. Using deductive reasoning, how many spider legs are in the box?
4.
Which type of reasoning is guaranteed to be true if the premises are true?
1. a)Inductive reasoning
2. b)Both types
3. c)Neither type
4. d)Deductive reasoning
5.
Is this reasoning deductive or inductive? 'I have seen 50 red apples. Therefore, all apples are red.'
1. a)Inductive, because it generalizes from the cases it has seen
2. b)Deductive, because all 50 apples are red
3. c)Deductive, because it reaches a rule about all apples
4. d)Neither, it is a proof, so the conclusion must be true
6.
'All fish live in water. Nemo lives in water. Therefore, Nemo is a fish.' Is this argument valid?
1. a)Yes, this is valid inductive reasoning
2. b)Yes, this is valid deductive reasoning
3. c)No, the premises are false
4. d)No, this is affirming the consequent
7.
All squares are rectangles. All rectangles have four sides. What can we conclude about squares?
8.
The pattern continues: 2, 6, 18, 54, ... What is the next number?
9.
One counterexample is enough to disprove a conclusion reached by which type of reasoning?
1. a)Both types equally
2. b)Neither type
3. c)Deductive reasoning
4. d)Inductive reasoning
10.
The crime happened at 9 PM downtown. Suspect A has a receipt proving they were at a grocery store across town at 9 PM. What can we conclude?
11.
A plant is 10 cm tall on Monday, 12 cm on Tuesday, 14 cm on Wednesday and 16 cm on Thursday. If the pattern continues, how tall will it probably be on Friday? (Answer in cm, number only)
12.
'If it rains, the streets get wet. The streets are wet. Therefore, it rained.' This is an example of:
1. a)Valid inductive reasoning
2. b)A true conclusion
3. c)A logical fallacy (affirming the consequent)
4. d)Valid deductive reasoning
13.
Analyze: 'No reptiles have fur. All snakes are reptiles. Therefore, no snakes have fur.' Is this valid?
14.
Which statement about valid arguments is TRUE?
1. a)A valid argument can have false premises but true conclusion
2. b)A valid argument always has true premises
3. c)Valid and true mean the same thing
4. d)A valid argument always has a true conclusion
15.
Create a valid deductive argument using these premises: 'All students in this class passed the exam' and 'Maria is a student in this class.'
16.
Ana tries the expression $n^2 + n + 41$ for $n = 1, 2, 3, 4, 5$ and gets 43, 47, 53, 61, 71, all prime numbers. She concludes: 'It gives a prime number for every whole number $n$ .' Which statement about her conclusion is true?
1. a)It is proven, because five cases agree
2. b)It can never be checked, because there are infinitely many numbers
3. c)It is an inductive guess, and it is false: for $n = 40$ the result is $41 \times 41$
4. d)It is deductive reasoning, so it must be true