# Find a pair set S such that: (a) S does not contain 0 and does not contain

## Question:

Find a pair set S such that: (a) S does not contain 0 and does not contain {0} either. (b) S contains 0 but does not contain {0}. (c) S does not contain 0 but contains {0}. (d) S contains both 0 and {0}.

2. Find a pair set S such that: (a) {1} does not belong to S and {1} is not a subset of S. (b) {1} belongs to S and {1} is not a subset of S. (c) {1} does not belong to S and {1} is a subset of S. (d) {1} belongs to S and {1} is a subset of S.

3. Consider three sets A, B and C such that: each one of these sets contains an element that does not belong to any of the other two sets; the three sets do not have any element in common; any two of them have at least one element in common. Illustrate these relationships with a Venn diagram.

4. (a) Find the set of all the subsets of {}. (b) Find the set of all the subsets of {{}}. (c) Find the set of all the subsets of {{0}. (d) Find the set of all the subsets of {{0,1}.

5. (a) What are the sets, if any, that do not have any subset? (b) What are the sets, if any, that have exactly one subset? (c) What are the sets, if any, that have exactly two subsets? (d) What are the sets, if any, that have exactly three subsets

6. Let A be the singleton {0}, the pair {0,1} and the triple {0,1,2}. (a) Find B×C and C×B. (b) Find B×A×C and (B×A×C. (c) Find B3 B2 ×B and B×B2

7. Consider three sets A, B and C. (a) When do we have B×C=C×B? (b) When do we have B×A×C=B×A×C?

8. Whenever possible, express each one of the following sets in the form of an integer interval and in the form of a real interval: ∅, {1}, N, N* Z, Z− Z* Z+ R, R− R* R+

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