0 votes 0 votes 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) $ Mathematical Logic mathematical-logic + – Dulqar asked Jan 7, 2017 Dulqar 707 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 3 votes 3 votes 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 saurabh rai answered Jan 7, 2017 • selected Jan 7, 2017 by Sushant Gokhale saurabh rai comment Share Follow See all 12 Comments See all 12 12 Comments reply Show 9 previous comments Sushant Gokhale commented Jan 7, 2017 reply Follow Share They have given example for 2005 question. Try it on your own. You will get it 0 votes 0 votes Sushant Gokhale commented Jan 7, 2017 reply Follow Share Even I find difficult taking examples. 0 votes 0 votes Dulqar commented Jan 7, 2017 reply Follow Share Actually tried some blunders here : https://gateoverflow.in/3783/gate2005-it-36?show=102140#c102140 0 votes 0 votes Please log in or register to add a comment.