GATE CSE 1995 | Question: 13

Question

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.

Comments

how you got this answer?

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Detailed Video Solution: https://youtu.be/B6xo-2A8ano?t=5776&feature=shared

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Propositional Logic Complete Summary & ALL GATE PYQs: https://youtube.com/playlist?list=PLgjejdknTfWNwpjPp4nYfxPbj5fqMeOsR&feature=shared 

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Use K-map

 

Answer 1

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

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

Comments

We can also minimize the expression right using K-Map?

(q V r) ∧ (p V ¬q).

Correct me if iam wrong.

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@AnilGoudar Canonical Conjunctive normal form is the maximized expression.and Conjunctive normal form is minimized expression.

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pls tell me how you get this expression? Iam getting another minimized form(1,5,6,7) i.e.(p^q)+(~q^r)

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thanks

Answer 2

$(p \vee \neg q\vee r)\wedge (p\vee \neg q\vee \neg r)\wedge (p\vee q\vee r)\wedge (\neg p\vee q\vee r)$

Answer 3

you could also plot a kmap since its only 3 variables finding the output for all the combination will  be easy task

Answer 4

It is contingency