0 votes 0 votes \[\exists(x)P(x) \Leftrightarrow \exists(x) \bar P(x)\] Mathematical Logic mathematical-logic first-order-logic engineering-mathematics + – Durgesh Singh asked Nov 20, 2017 Durgesh Singh 403 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply Shubhanshu commented Nov 20, 2017 reply Follow Share Take a variable x1 which have p(x) is true then its !P(x) will false, thus it is true <-> false. Hence above is not true. 1 votes 1 votes Durgesh Singh commented Nov 20, 2017 reply Follow Share Let P(x) = x eats meat. ∃(x)P(x) means some people eat meat. Can't we say that from set of all people ..if some people eat meat then some people do not eat meat.Please advise where I am wrong. 0 votes 0 votes Shubhanshu commented Nov 20, 2017 reply Follow Share ∃(x)P(x) means some people eat meat First if you want to apply this predicate to set of people then you should use Domain of Discourse as people. Because if Domain is not mentioned then this statement is applied over all entity of the universe. Ref:-https://en.m.wikipedia.org/wiki/Domain_of_discourse Refer the example section. 0 votes 0 votes Durgesh Singh commented Nov 20, 2017 reply Follow Share Ok is it true if we define domain of discourse as set of all living people? 0 votes 0 votes Please log in or register to add a comment.