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21 votes
21 votes
Obtain the principal (canonical) conjunctive normal form of the propositional formula $$(p \wedge q) \vee (\neg q \wedge r)$$ where $\wedge$ is logical and, $\vee$ is inclusive or and $\neg$ is negation.
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Best answer
38 votes
38 votes

Note:-

  1. Canonical conjunctive normal form means in our Digital logic it is Canonical Product of Sum term Form.
  2. Canonical Disjunctive normal form means in our Digital logic it is Canonical Sum of Product term Form.

$pq+q'r$
Putting in $\text{k-map},$ we will get

$\sum(1,5,6,7)= \prod(0,2,3,4)=(p\vee q\vee r) \wedge (p\vee¬q\vee r) \wedge (p\vee¬q\vee¬r) ∧ (¬p\vee q\vee r)$

edited by
10 votes
10 votes
$(p \vee \neg q\vee r)\wedge (p\vee \neg q\vee \neg r)\wedge (p\vee q\vee r)\wedge (\neg p\vee q\vee r)$
0 votes
0 votes
you could also plot a kmap since its only 3 variables finding the output for all the combination will  be easy task

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