GATE CSE
First time here? Checkout the FAQ!
x
0 votes
82 views
There is a student in the class who has sent an e-mail to everyone else in the class,Consider domain as all students in a class.

Assume M(x,y) means x has send an email to y

 

Answer given is :-  ∃x∀y[(x≠y)→M(x,y)]

 it's gonna result in True if the x=y  and the student has sent himself an email

Shall we use ^ consider instead of -> ?Please correct
asked in Mathematical Logic by Active (2.4k points)  
edited by | 82 views
You use ^ whe you need to test the clauses independently.

When x=y, M(x,y)=false . So, the result is true and this precisely what we want, right?
But question says everyone else. So how this is true for a person sending to himself?
F -> F is true ,right?
What i am getting is that a student who has sent mail to everyone else in class means everyone else except him and thats why i am getting confused whether he has sent mail to himself or not?

If he has sent then F->F will be true else we will use ^.Please clear this point
Consider the that Rahul sends mail to everyone except himself. Now, let the sql table describing the information be:

student in class             Has been sent mail

-----------------------------------------------------------------------

Sushant                          Yes

Arjun                               Yes

Rahul                               No

 

Now, what functional dependency would you derive to describe the students that have been sent mail by Rahul?

Note that in ^ operator, you need to test the operands of ^ independently while for ->, you need to check only the premise.
I am asking that whether we should consider that a person has sent a mail to himself or not

Two possible answers :

1.   ∃x∀y[(x≠y)→M(x,y)] :- In this ,it will be true even when x=x,as implication becomes true,So there exits a student who has sent a mail to everone(including himself)

2.  ∃x∀y[(x≠y)^M(x,y)]:-This means there is a student who has sent a mail to everyone except himself.

Nowthe only difference is 1. answer allowing x=x,where as second is not.

But what actually is implied by the question i am not getting
No, if ^ is used it says only x exist in the class.
^ specifies the properties of selected things from the sql table(if there exists one), right Arjun?
@Arjun Sir, it will not say only x exist,it will say at least one x exist for all y.Please correct

Please log in or register to answer this question.

Top Users Jan 2017
  1. Debashish Deka

    7906 Points

  2. Habibkhan

    4736 Points

  3. Vijay Thakur

    4474 Points

  4. sudsho

    4318 Points

  5. saurabh rai

    4200 Points

  6. Arjun

    3638 Points

  7. Bikram

    3500 Points

  8. santhoshdevulapally

    3480 Points

  9. GateSet

    3228 Points

  10. Sushant Gokhale

    3116 Points

Monthly Topper: Rs. 500 gift card

18,944 questions
23,897 answers
52,122 comments
20,213 users