MATH 1090.03D

Fall 2000

Date posted: Nov. 1, 2000 Due: In the first tutorial immediately following the end of the CUPE strike

Alternative Problem Set No. 3—On Chapter 3 and 4 of “GS”. See also our “Web–Ch.1”.

This problem set is an alternative set to the one collected today.

It is ONLY FOR THOSE students who exercised their right of choice not to cross the picket lines, and therefore did not attend classes during the strike.

Only ONE problem set #3 will be accepted. Please ignore this problem set IF you have already handed in the original problem set #3.

• Do the following problems from the text, Chapter 3.

For the following Chap.3-problems you must use the equational style of Chapter 3 of “GS”.

3.36, 3.39, 3.40, 3.46, 3.54, 3.60, 3.68, 3.70, 3.71, 3.72.

Hint for the above. Ignore ALL hints!

• In this exercise use the Deduction Theorem and, if helpful, the “cut rule” as your central tools—but do not use the “Tautology Theorem” (Post’s [completeness] theorem). Prove (where A, B, C are any given wffs):

(1) ⊢ (A ⇒ B) ⇒ (A ∨ C) ⇒ (B ∨ C)

(2) ⊢ (A ⇒ B) ⇒ (C ⇒ A) ⇒ (C ⇒ A ∨ B).

• In this exercise you are allowed to use Post’s Tautology Theorem (and any other “valid” tools we have “built” in class, e.g., soundness, Deduction theorem, Cut rule, etc.).

For any A, B (wffs) do (1) below:

(1) True or false, and WHY? A ∨ B ⊢ A ∧ B

(2) Also do, Ch. 4, p.80, 4.1, 4.2, 4.7.