GATE CSE
First time here? Checkout the FAQ!
x
0 votes
102 views

Is the given statement True ?  Please explain

  • $\forall_x \left \{ P(x) \vee Q(x) \right \}\Leftrightarrow \forall_x P(x) \vee \forall_x Q(x) $
  • $\forall_x \left \{ P(x) \wedge Q(x) \right \}\Leftrightarrow \forall_x P(x) \wedge \forall_x Q(x) $
  • $\exists_x \left \{ P(x) \vee Q(x)\right \} \Leftrightarrow \exists_x P(x) \vee \forall_x Q(x)$
  • $\exists_x \left \{ P(x) \wedge Q(x) \right \}\Leftrightarrow \exists_x P(x) \wedge \exists_x Q(x) $
asked in Mathematical Logic by Loyal (2.6k points)   | 102 views

1 Answer

+3 votes
Best answer
Only 2nd and third is true
∀ is true when it is true for each nd every value of its domain so it is distributive on AND
∃ is true when it is true for atleast value of its domain  so it is distributive on OR
answered by Veteran (10.7k points)  
selected by
Either try with examples or you need to prove it(which is difficult)

Its hard for me try with examples also :( 
Is there any other approach ?

Can u just show for this http://gateoverflow.in/3783/gate2005-it-36

How to check other options using examples ? :( 
Sorry i was asking too much questions . I was not able to understand this topic at all

They have given example for 2005 question. Try it on your own. You will get it
Even I find difficult taking examples.


Top Users Jun 2017
  1. Bikram

    3912 Points

  2. Arnab Bhadra

    1550 Points

  3. Hemant Parihar

    1502 Points

  4. Niraj Singh 2

    1501 Points

  5. Debashish Deka

    1480 Points

  6. junaid ahmad

    1432 Points

  7. pawan kumarln

    1366 Points

  8. Arjun

    1246 Points

  9. Rupendra Choudhary

    1242 Points

  10. rahul sharma 5

    1240 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 Jun 26 - Jul 02
  1. pawan kumarln

    498 Points

  2. akankshadewangan24

    404 Points

  3. Arjun

    286 Points

  4. Debashish Deka

    234 Points

  5. Abhisek Das

    230 Points


23,435 questions
30,153 answers
67,633 comments
28,503 users