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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 Active (1.9k points)   | 83 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 Boss (9.5k 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.

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