Kenneth Rosen Edition 6th Exercise 1.3 Question 41b (Page No. 49)

Question

Express each of these system specifications using predicates,
quantifiers, and logical connectives

b) Whenever there is an active alert, all queued messages
are transmitted.

There are two Solution to this 
AND

Both seems correct to me . Which is good.

But one of my friend argues :-
 a(x) x is an active alert
q(m) m is a queued message
t(m) message m is transmitted
∃(a(x)AND ∀m( q(m)->t(m))
And the reason " we don't use implication with ∃x "

Which leaves me in confusion.?

Answer 1

There are two Solution to this  

Only First Solution is Correct  i.e.

is Correct only.

Second Solution is Wrong for the given statement. i.e.

is Wrong for the given specification.

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But one of my friend argues, ∃(a(x)AND ∀m( q(m)->t(m)) 

This is Wrong as well for the given specification.

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Given specification is of the form "If ------ then"..So, Only First Solution is Correct. 

Comments

One must know the whole meaning of "we can't use implication with there exists"

where we can use there exists with implication??

Can u elaborate? 

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In Rosen, in some questions implications are used with there exists 
For example 1.4 question 8 
option C

So where to use implication with there exists, where not ??

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@Dee, according to what i understand from your comments
There is " if...then" part therefore you have to choose option D as answer...
If the sentence is " whenever it is a rat, x is hop " then ans is option c.

Correct me if i am wrong