MA-351 Homework 4
Due Thurs. Nov. 18, at 23:59pm.
All solutions must be submitted on the Moodle web site
for the class at wolfware.ncsu.edu.
You may upload a photo of your handwritten solution or
a file of your typed solution.
Note my office hours on my
schedule.
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Consider the Boolean expression
((a implies b) nand c) xor ((a xor b) or c)
where
x implies y is the implication operator (not x) or y,
x equiv y is the equivalence operator [(x and y) or ((not x) and (not y))],
x xor y is the exclusive or operator not (x equiv y),
and x nand y is the Sheffer stroke not (x and y).
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Find a CNF (with k clauses and no more than 3 literals per clause)
that is equivalent to this expression.
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Draw the graph corresponding to the CNF that has
a clique of size k if and only if the CNF is satisfiable.
For a satisfying assignment, identify the corresponding clique.
-
Please write a Boolean expression
in the variables
a
and
b
using only the nand operator
that is equivalent to a xor b.
[Hint: for a short answer, start with
a xor b as
not (not ((a and (not b)) or ((not a) and b) ) ).]