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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) $

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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
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