in Mathematical Logic edited by
3,651 views
19 votes

Which of the following is/are a tautology?

  1. $a \vee b \to b \wedge c$
  2. $a \wedge b \to b \vee c$
  3. $a \vee b \to \left(b \to c \right)$
  4. $a \to b \to \left(b \to c \right)$
in Mathematical Logic edited by
3.7k views

Subscribe to GO Classes for GATE CSE 2022

2 Answers

22 votes
 
Best answer

Answer: (B)

$\left(a \wedge b \right) \to b \vee c$
$\implies \neg \left(a \wedge b \right) \vee b \vee c$
$\implies \neg a \vee \neg b \vee b \vee c$
$\implies T$

Option (A) is not TRUE when $c$ is FALSE.
Option (C) is not TRUE when $b$ is TRUE and  $c$ is FALSE.
Option (D) is not TRUE when $a$ and $b$ are TRUE and $c$ is FALSE.

edited by

11 Comments

edited by
When I am solving option (b) , after simplification , I get  (~a +1+ c ) . So , for a=1 , b=0 , c=0 , output is 1.

and when I solve option (d) , after simplification I get (~a+~b+c) .

So , option (b) is tautology
1
Tautology means after simplification you should get TRUE.
1
ohkk , my mistake.. sorry .. Thanks a lot.
0

How to treat option D? (the associtivity)  a->(b->(b->c)) or (a->b)->(b->c)

6
Is not option (d) ambiguous?
2
Take it either way - both are not tautology for option D.
4
2
@Arjun any of the associativity work for this problem. But in general what is the associativity?
1

Associativity like

Not>AND>OR>IMPLICATION 

  • AND,OR is left associative .
  • Implecation is right associative
5

Associativity like

Not>AND>OR>IMPLICATION 

You mean Precedence of the Operator rt? 

0
@arjun sir can you please telll me precedence of these operations
0
8 votes

Option b is tautology.

2 Comments

@abhishekmehta4u

Nice approach

1

@abhishekmehta4u your approcah is good and all, but a minor mistake in the (A) part :

You accidentally wrote the R.H.S  of (A) as ($b \vee c$ )instead of ($b \wedge c$)

0
Answer:

Related questions

Ask
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