This preview shows page 1. Sign up to view the full content.
CS 2603
— A
PPLIED
L
OGIC
FOR
H
ARDWARE
AND
S
OFTWARE
9/26/07
Midterm Examination 1
Fall 2007
1
Consider the following proposition.
(((a
∨
b)
∧
(b
∨
c))
∧
(
¬
b))
a) How many rows would a truth table for the proposition have?
c) Classify the proposition as satisfiable, tautology, or contradiction.
2
a) Diagram a digital circuit representing the proposition of problem 1.
b) Rewrite the proposition of problem 1 in proofchecker notation.
3
a) Supply the missing details in this proof. Assume it cites inference rules only, not theorems.
b) Draw a box around each discharged assumption.
c) State the theorem that the proof confirms.
Use natural deduction to prove the following theorems, citing inference rules or theorems
stated in the form of inference rules on the cribsheet.
4a
→
(b
→
c)

(a
∧
b)
→
c
5(
b
∨
c)
∧
a

(a
∧
b)
∨
(a
∧
c)
Prove the following equations using
the laws and theorems of Boolean algebra stated on the
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 RexPage

Click to edit the document details