34 l;l Theory of Computer Science
1.12 Is the implication (P i\ (P ~ ---, Q)) v (Q ~ ---, Q) ~ ---, Q a tautology?
1.13 Obtain the principal disjunctive normal form of the following:
(a) P ~ (P ~ Q i\ (---, (---, Q v ---, P)))
(b) (Q i\ ---, R i\ ---, S) v (R i\ S).
1.14 Simplify the formula whose principal disjunctive normal form is
110 v 100 v 010 v 000.
1.15 Test the validity of the following arguments:
(a) P ~ Q
R=> -,Q
:. P =>-,R
(b) R ~ ---, Q
P~Q
-,R => S
:. P => S
(c) P
Q
---,Q ~ R
Q=> ---,R
:. R
(d) P ~ Q i\ R
Q v S ~ T
SvP
:. T
1.16 Test the validity of the following argument:
If Ram is clever then Prem is well-behaved.
If Joe is good then Sam is bad and Prem is not well-behaved.
If Lal is educated then Joe is good or Ram is clever.
Hence if Lal is educated and Prem is not well-behaved then Sam is bad.
1.17 A company called for applications from candidates, and stipulated the
following conditions:
(a) The applicant should be a graduate.
(b) If he knows Java he should know C++.
(c) If he knows Visual Basic he should know Java.
(d) The applicant should know Visual Basic.
Can you simplify the above conditions?
1.18 For what universe of discourse the proposition '\Ix (x ~ 5) is true?
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