EXERCISES
1. A very deep connection (an isomorphism) exists between set operations and the logical connectives in the propositional logic.
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Operation
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Propositional Logic
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Set Theory
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Disjunction
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Or
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Union
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Conjunction
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And
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Intersection
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Negation
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Not
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Complement
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Implication
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If, Then
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Subset
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Exclusive or
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Symmetric difference
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a. Express A ⊕ B in words.
b. Express (A ≈ B) - (A ∩ B) in words.
c. Convince yourself that A ⊕ B and (A ≈ B)- (A ∩ B) are the same set.
d. Is it true that A ⊕ B = (A - B) ≈ (B - A)?
e. What name would you give to the blank entry in the previous table?
2. In many parts of the United States, real estate taxes are levied by different taxing bodies, for example, a school district, a fire protection district, a township, and so on. Discuss whether these taxing bodies form a partition of a state. Do the 50 states form a partition of the United States of America? (What about the District of Columbia?)
3. Is brotherOf an equivalence relation on the set of all people? How about siblingOf?