A very deep connection an isomorphism exists between set

EXERCISES

1. A very deep connection (an isomorphism) exists between set operations and the logical con­nectives in the propositional logic.

 Operation Propositional Logic Set Theory Disjunction Or Union Conjunction And Intersection Negation Not Complement Implication If, Then Subset Exclusive or Symmetric difference

a. Express 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?