GATE CSE
First time here? Checkout the FAQ!
x
0 votes
98 views
Represent using logic connectives :-

1. "Whenever there is an active alert, all queued messages are transmitted."

Given answer is :-∃x(Alert(x)∧Active(x))→∀y((Message(y)∧Queued(y))→Transmitted(y))

2. Purple mushrooms are poisonous

∀x( purple(x)∧mushroom(x)→ Poisonous(x) )

I need to ask that in first statement why are we using ∃x instead of ∀ in the beginning . I mean it should be same as If there is an active alert then do XYZ.Like in second statement. If i use ∀ in the begriming then it will become "For every object x in universe if x is an active alert then queued messages are transmitted". What is wrong in this?

so ∀(Alert(x) ^ Active(x) -> XYZ).

Why are we using  ∃ in the start.?

asked in Mathematical Logic by Boss (9.7k points)  
edited by | 98 views

1 Answer

0 votes
"Whenever there is an active alert, all queued messages are transmitted."

Whenever -> Condition Statement.

There is... -> Existential condition.

All -> Universal condition.

So it becomes:

"If there is an active alert, all queued messages are transmitted" -> If there exists an alert which is active, then if for every message which is queued then the message is transmitted."

I translated the conditional and quantifiers perfectly, there may be some mistake in English but that's not important.

answered by (171 points)  


Top Users Aug 2017
  1. Bikram

    5174 Points

  2. ABKUNDAN

    4730 Points

  3. akash.dinkar12

    3504 Points

  4. manu00x

    3492 Points

  5. rahul sharma 5

    3188 Points

  6. makhdoom ghaya

    2700 Points

  7. just_bhavana

    2432 Points

  8. stblue

    2244 Points

  9. Tesla!

    2090 Points

  10. pawan kumarln

    1874 Points


25,065 questions
32,220 answers
75,083 comments
30,231 users