Homeworks
Homework 1 (Due: Thursday, Feb. 2 before class)
1. A set of propositions is consistent if there is an assignment of truth values to each of the variables
in the propositions that makes each proposition true. Is the following set of propositions consistent?
The system is in multiuser state if and only if it is operating normally.
The system is operating normally only if the kernel is functioning.
The kernel is not functioning or the system is in interrupt mode.
The system is in interrupt mode whenever it is not in multiuser state.
The system is in interrupt mode.
2. Find a proposition with three variables ??, ??, and ?? that is:
a) never true.
b) never false.
c) false, only when ?? = ??, ?? = ?? and ?? = ??.
d) true, only when all variables are false.
3. Exercise 34 on page 25 in the textbook.
4. Show that ,?? ? ??) ? (?? ? ÿ) and ?? ? ?? are logically equivalent without using a truth table.
5. Find the Principal Disjunctive Normal Form and the Principal Conjunctive Normal Form for the
following proposition: (?? ? ??) ? (ÿ ? ??).
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