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+1 vote

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 v~q

p ∨ ~p is always true

a is a tautology


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


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


C  a and b

answered by Veteran (30.2k points) 107 371 691

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