Awesome q2a theme
0 votes
20 views

which of the following options are equivalent to statement?

 

in Mathematical Logic by (45 points) | 20 views
+1
option A
0
correct, how did you do it...

1 Answer

0 votes
Best answer

$\forall xP(x) \vee \exists yP(y)$ is true

$\implies$ either $\forall xP(x)$ is true or  $\exists yP(y)$ is true …..$(i)$

 

Now, if $P(x)$ is true for all $x$ then $P(x)$ will be true for some $x$ also right ?

i.e. $\exists xP(x)$ is true , put this in eq $(i)$

$\implies$ either $\exists xP(x)$ is true or  $\exists yP(y)$ is true

$\implies \exists xP(x) \vee \exists yP(y)$ is true

write $x$ in place of $y$

$\implies \exists xP(x) \vee \exists xP(x)$ is true

$\implies \exists xP(x) $ is true

$\therefore$ Option A is correct.

by (3.7k points)
selected by
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
Welcome to GATE CSE Doubts, where you can ask questions and receive answers from other members of the community.
Top Users Dec 2019
  1. Pratyush Priyam Kuan

    164 Points

  2. Vimal Patel

    120 Points

  3. avistein

    65 Points

  4. srestha

    54 Points

  5. Mk Utkarsh

    49 Points

  6. arya_stark

    46 Points

  7. goxul

    39 Points

  8. Sathuri Bharath

    34 Points

  9. vishal burnwal

    32 Points

  10. Shaik Masthan

    28 Points

Monthly Top User and those within 60% of his/her points will get a share of monthly revenue of GO subject to a minimum payout of Rs. 500. Current monthly budget for Top Users is Rs. 75.
2,317 questions
1,295 answers
6,601 comments
89,719 users