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)Deductive reasoning
2. b)Creative thinking
3. c)Inductive reasoning
4. d)Random guessing
2.
In a syllogism, what do we call the statements that are assumed to be true?
1. a)Questions
2. b)Conclusions
3. c)Premises
4. d)Hypotheses
3.
Premise 1: All birds have feathers. Premise 2: A robin is a bird. Conclusion: A robin has ___.
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)8 is divisible by 2
3. c)2 is an even number
4. d)8 is divisible by 3
5.
Premise 1: If it snows, school is closed. Premise 2: It is snowing. Conclusion: School is ___.
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)All triangles have 3 sides. This shape has 3 sides. Therefore, this shape is a triangle.
3. c)If it rains, the grass is wet. The grass is wet. Therefore, it rained.
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?
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)Dr. Smith studies logic
2. b)Some mathematicians study philosophy
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 is a reptile. Does a lizard have fur? (Answer yes or no)
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 squares have 4 sides. This shape is a square. Therefore, it has 4 sides.
3. c)If it rains, I get wet. I am wet. Therefore, it rained.
4. d)All fish can fly. Salmon is a fish. Therefore, salmon can fly.