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HW 12
Intermediate Logic
Spring 2007
1. LPL 15.12
2. LPL 15.13
3. LPL 15.17
4. The difference between two sets A and B is the set of all objects that belong to set
A but not to B. This is written as A \ B
a. Provide a definitional axiom for A \ B (use a 2-place function symbol
diff(x,y))
b. Construct a formal proof that shows that for any sets A, B, and C:
A  (B \ C) = (A  B) \ C
5. Any set without any elements is an empty set
a. Provide a definitional axiom that defines a 1-place predicate Empty(x)
expressing that x is an empty set
b. Construct a formal proof that shows that there exists exactly one empty
set. (hint: use axioms of Extensionality and Comprehension, but without
deriving Russell’s contradiction!)
Do problems 1, 2, and 3 in Fitch and submit to the Grade Grinder. Problems 4 and 5 can
be done in either Fitch or NDL. Feel free to make any ‘reasonable’ use of Taut Con (and
whatever goes for that in NDL). This HW is due Friday April 6.