Set Theory Practice Worksheet PDF

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Dr. Stephanie Andrews...

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Math 1332

Practice - Set Theory

Jorge Galvan Name___________

Determine whether each statement is true or false. Justify your answer with at least one sentence.

1. {5} ∈ {1, 2, 3, 4, 5, 6, 7}

This is True because the number 5 is in the set.

2. If A = { x | x is a day of the week} and B= {2, 4, 6, . . ., 14}, then sets A and B are equivalent.

This is True because set A contains 7 elements per the days of the week, and set B also contains 7 elements. 3. {2, 4, 6, 8} = {#, &, *, @}

This is False because the second set has symbols that don’t equal the numbers in the first set. 4. {d, e, f, g} ⊆ {a, b, c, d, e, f}

This is False because the statement claims that the first set is a subset of the second set. The letters d,e, and f are in the second set but not the letter g.

5. {3, 4, 5} ⊂ { x | x ∈ N and x < 6} This is True because the numbers 3,4, and 5 are natural numbers that are less than 6, which is what the statement says. 6. 14 ∉ {1, 2, 3, 4, . . . 39, 40}

This statement is False because the number 14 is included in the set.

For the following exercises let

U = {a, b, c, d, e, f, g} A = {a, b, c, d} B = {c, d, e, f} C = {a, e, g}

Find each of the following sets of cardinalities. Be sure to use the appropriate notation.

7. A ∪ B

= { a,b,c,d,e,f }

8. (B ∩ C )’ = { c,d,f,a,g }

9. A ∩ C’

= { b,c,d,e,g }

10. Refer to the diagram below to answer the questions.

{ 5,8 }

{ 3,4,5,6,7,8 }

{ 3,4,6 }

{ 1,2,3,4,5,6,7,8 }

{8}...