MATH 1090.03D

Fall 2000

Date: Oct. 16, 2000 Due: Oct. 30, 2000—▶In class—NO papers will be accepted after 11:45am◀ Problem Set No. 3—On Chapter 3 and 4 of “GS”. See also our “Web–Ch.1”.

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

3.35, 3.37, 3.55, 3.56, 3.58, 3.61, 3.62, 3.63, 3.64, 3.67. Hint for the above. Ignore the 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”. Prove (where A, B, C are any given wffs):

(1) ⊢ A ⇒ B ⇒ A ∧ B

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

• In this exercise you are allowed to use Post’s Tautology Theorem (and any other “valid” tools we have “built” in class).

Prove for any A, B, C (wffs) that (1) ⊢ (A ∧ B ⇒ C) ≡ (A ⇒ B ⇒ C)

(2) Also do, Ch. 4, p.80, 4.2, 4.5, 4.12.