Deductive Reasoning

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Show your work for each problem.

1.
What type of reasoning starts with general statements and reaches specific conclusions?
1. a)Random guessing
2. b)Creative thinking
3. c)Inductive reasoning
4. d)Deductive reasoning
2.
In a syllogism, what do we call the statements that are assumed to be true?
1. a)Questions
2. b)Premises
3. c)Conclusions
4. d)Hypotheses
3.
Premise 1: Every spider has 8 legs. Premise 2: Charlotte is a spider. How many legs does Charlotte have?
4.
Premise 1: All even numbers are divisible by 2. Premise 2: 8 is an even number. What can you conclude?
1. a)8 is an odd number
2. b)2 is an even number
3. c)8 is divisible by 2
4. d)8 is divisible by 3
5.
Premise 1: All triangles have 3 sides. Premise 2: Shapes A, B and C are triangles. How many sides do the three shapes have in total?
6.
Premise 1: All rectangles have four right angles. Premise 2: A square is a rectangle. What can you conclude about a square?
7.
Which of the following is a logical fallacy (incorrect reasoning)?
1. a)If A then B. A is true. Therefore, B is true.
2. b)If it rains, the grass is wet. The grass is wet. Therefore, it rained.
3. c)All triangles have 3 sides. This shape is a triangle. Therefore, this shape has 3 sides.
4. d)All dogs are mammals. Rex is a dog. Therefore, Rex is a mammal.
8.
Premise 1: If a number is divisible by 6, it is divisible by both 2 and 3. Premise 2: 18 is divisible by 6. What can you conclude about 18?
9.
Premise 1: All prime numbers greater than 2 are odd. Premise 2: 7 is a prime number greater than 2. Is 7 odd or even?
1. a)It cannot be determined
2. b)Odd
3. c)Both odd and even
4. d)Even
10.
A valid deductive argument with true premises will always have:
1. a)A true conclusion
2. b)A false conclusion
3. c)Multiple conclusions
4. d)An uncertain conclusion
11.
Premise 1: If a polygon is regular, all its sides are equal. Premise 2: If all sides of a polygon are equal and it has 4 sides, it is a rhombus. Premise 3: Figure X is a regular polygon with 4 sides. What is Figure X?
12.
Premise 1: All mathematicians study logic. Premise 2: Some people who study logic also study philosophy. Premise 3: Dr. Smith is a mathematician. What can we definitely conclude?
1. a)Some mathematicians study philosophy
2. b)Dr. Smith studies logic
3. c)Dr. Smith studies philosophy
4. d)Dr. Smith does not study philosophy
13.
Premise 1: No reptiles have fur. Premise 2: All mammals have fur. Premise 3: A lizard, a snake and a turtle are reptiles; a dog and a rabbit are mammals. How many of these five animals have fur?
14.
Premise 1: If today is Monday, then tomorrow is Tuesday. Premise 2: If tomorrow is Tuesday, then the day after tomorrow is Wednesday. Premise 3: Today is Monday. What day is the day after tomorrow?
15.
Which of the following arguments is both VALID and SOUND (has true premises and correct logic)?
1. a)Some birds can swim. Penguins are birds. Therefore, penguins can swim.
2. b)All fish can fly. Salmon is a fish. Therefore, salmon can fly.
3. c)If it rains, I get wet. I am wet. Therefore, it rained.
4. d)All squares have 4 sides. This shape is a square. Therefore, it has 4 sides.