Discrete Structures, Logic, and Computability, 4th Edition

chapter 8

Section 8.1

1.

2. a.

3. Use the composition rule (8.1.3) applied to a sequence of three statements.

a.

4. a. First, prove $\left\{(x<10)\wedge (x\ge 5)\right\}x:=4\{x<5\}:$

Second, prove that (x < 10) ∧ ¬ (x ≥ 5) → (x < 5). This is a valid wff because of the equivalence ¬ (x ≥ 5) ≡ (x < 5). Thus the original wff is correct, by the if-then rule.

c.