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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 Veteran (15k points) 13 109 316
edited by | 119 views

1 Answer

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"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 (483 points) 1 10


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