GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
151 views

Consider the compund propositions given below as:

  1. $p \vee \sim (p \wedge q)$
  2. $(p \wedge \sim q) \vee \sim (p \wedge q)$
  3. $p \wedge (q \vee r)$

Which of the above propositions are tautologies

  1. a and c
  2. b and c
  3. a and b
  4. a, b, and c
asked in Mathematical Logic by Veteran (92.5k points) 964 2327 3113
recategorized by | 151 views

2 Answers

+6 votes
Best answer
$p\vee (p\wedge q)`$ = p+p`+q` = 1+q`= 1 so tautology.

C and b cant be tautology so no option is matching.
answered by Veteran (52.8k points) 21 71 325
selected by
How b. Is tautology
only a is tautology but since c nver be tautology so i choose b .
–1 vote

p∨~(p∧q)

p∨~(p∧q) =p ∨ ~p v~q

p ∨ ~p is always true

a is a tautology

 (p∧~q)∨~(p∧q)

(p∧~q)∨~(p∧q) = (p∧~q)∨(~pv~q) is also tautology

 p∧(q∨r)

 p∧(q∨r) =  (p^q) v (p^r) is not a tautology

Answer 

C  a and b

answered by Veteran (30.2k points) 107 371 691


Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
Top Users Oct 2017
  1. Arjun

    23338 Points

  2. Bikram

    17048 Points

  3. Habibkhan

    7912 Points

  4. srestha

    6238 Points

  5. Debashish Deka

    5438 Points

  6. jothee

    4968 Points

  7. Sachin Mittal 1

    4772 Points

  8. joshi_nitish

    4286 Points

  9. sushmita

    3964 Points

  10. Rishi yadav

    3794 Points


Recent Badges

Popular Question user1234
Copy Editor Ayush Upadhyaya
Popular Question asu
Popular Question .
Popular Question makhdoom ghaya
Popular Question junaid ahmad
Notable Question learner_geek
Notable Question jothee
Popular Question jothee
Notable Question Jeffrey Jose
27,290 questions
35,142 answers
83,926 comments
33,231 users