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MA 110 Test 1: Logic and Set Theory Questions, Exercises of Mathematical Methods for Numerical Analysis and Optimization

Baddi University of Emerging Sciences and TechnologiesMathematical Methods for Numerical Analysis and Optimization

The questions and answers for a test in logic and set theory. The test covers various topics such as venn diagrams, symbolic logic, set operations, and counting. Students are required to use logical reasoning and mathematical concepts to solve the problems. The document also includes points allocated to each question.

Typology: Exercises

2012/2013

Uploaded on 03/31/2013

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MA 110-91
§1.1 – 3.1 Test #1 score
Name:
30 September 2000
1. Use a properly labeled Venn diagram to determine the validity of the following argument.
Explain. (9 points)
1. All nurses are caring.
2. Jill is caring.
Therefore Jill is a nurse.
2. Convert the following argument into symbolic form and determine if the argument is
valid using a truth table. (10 points)
If math is interesting, then I’ll get an A. If I study well, then I’ll get an A. I get an
A. Therefore, I studied well or math is interesting.
3. Write the contrapositive of the statement "If I get an A or a B then I will be happy." (8 points)
pf3

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Download MA 110 Test 1: Logic and Set Theory Questions and more Exercises Mathematical Methods for Numerical Analysis and Optimization in PDF only on Docsity!

MA 110-

Test

score

Name:

30 September 2000

  1. Use a properly labeled Venn diagram to determine the validity of the following argument. Explain. (9 points) 1. All nurses are caring. 2. Jill is caring.

Therefore Jill is a nurse.

  1. Convert the following argument into symbolic form and determine if the argument is valid using a truth table. (10 points)

If math is interesting, then I’ll get an A. If I study well, then I’ll get an A. I get an A. Therefore, I studied well or math is interesting.

  1. Write the contrapositive of the statement "If I get an A or a B then I will be happy." (8 points)

MA 110 Test 1 page 2

  1. If U = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 }, A = { 1 , 3 , 5 , 7 , 9 } and B = { 1 , 2 , 3 , 4 , 5 , 6 }, find the set A ∩ B ; then find (A ′^ ∪ B ′ ) ′. (9 points)
  2. How many subsets are there of a set having 8 elements? Explain how the answer is related to the number of ways a hamburger can be served if there are 8 different condiments for the customer to choose from. (9 points)
  3. In a dorm holding 1000 students, 500 are taking math, 300 are taking biology, and 200 are taking a foreign language. Suppose 25 are taking all three, 75 are taking math and biology, 50 are taking only a foreign language, and 65 are taking math and a foreign language. What percentage of students in the dorm are taking at least one of these three subjects? Draw and label a Venn diagram and explain your reasoning. (10 points)
  4. Compute the numbers 8 P 5 and 8 C 5. Explain these numbers would be used in a counting argument. (9 points)