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 667 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 Dulqar commented Jan 7, 2017 reply Follow Share Can u tell why 4 is true ? with some reason / example .? Im not able to understsand that situation 0 votes 0 votes saurabh rai commented Jan 7, 2017 reply Follow Share bt 4 is nt true 0 votes 0 votes saurabh rai commented Jan 7, 2017 reply Follow Share ∃x p(x)∧∃x q(x) and ∃x (p(x)∧q(x)) suppose domain consist of all positive integers p(x)= x is odd q(x)= x is even consider ∃x p(x)∧∃x q(x) ,it is saying that there exist odd numbers and there exist even numbers now consider ∃x (p(x)∧q(x)) it is saying that there exist a no. which is is both odd and even it is trivially false. 2 votes 2 votes Sushant Gokhale commented Jan 7, 2017 reply Follow Share @Dq. P: Divisible by 2 Q: Divisible by 3 And let x={2,4,8} For this 4th statment is F$\Leftrightarrow$ T 1 votes 1 votes Dulqar commented Jan 7, 2017 reply Follow Share Got it :) Thanks. Can I ask one more question ? 0 votes 0 votes Sushant Gokhale commented Jan 7, 2017 reply Follow Share yes bro 0 votes 0 votes Dulqar commented Jan 7, 2017 reply Follow Share How to solve these kind of questions ? https://gateoverflow.in/3783/gate2005-it-36 https://gateoverflow.in/256/gate1992_92-xv Some Resources I have seen some of the options is proved by CP or IP rule and some options by examples . I m not getting a general idea how to deal with these kinda questionz :( 0 votes 0 votes Sushant Gokhale commented Jan 7, 2017 reply Follow Share Either try with examples or you need to prove it(which is difficult) 1 votes 1 votes Dulqar commented Jan 7, 2017 reply Follow Share Its hard for me try with examples also :( Is there any other approach ? Can u just show for this https://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 0 votes 0 votes 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.