Predicate logic inference problem

[akshayms]

Homework Statement

Consider the following question

Adams is a boy who does not own a car. Mary dates only boys who own
cars.Therefore Mary does not date Adams.

Homework Equations

The Attempt at a Solution

My answer is like this...
Let Bx=x is a boy.
Ox=x owns car
Dxy=x Dates y
a=Adams
m=Mary
Accordingly we can translate sentences as


1)Ba&~Oa
2)for all x (Bx&Ox->Dmx)
-----------------------
2) can be written as Ba&Oa->Dma (by universal specification)
further 2 can be reduced to
3) Ba->(Oa->Dma) (By law of exportation)
4) Oa->Dma (from p->q and p so q)
5) ~Oa (From p&q so q)
So, "we can't conclude that Mary does not date Adams".

Am i wrong? If I'm please explian me where it went wrong. Thanks in advance.

 

[Mark44]

Homework Statement

Consider the following question

Adams is a boy who does not own a car. Mary dates only boys who own
cars.Therefore Mary does not date Adams.

Homework Equations

The Attempt at a Solution

My answer is like this...
Let Bx=x is a boy.
Ox=x owns car
Dxy=x Dates y
a=Adams
m=Mary
Accordingly we can translate sentences as


1)Ba&~Oa
2)for all x (Bx&Ox->Dmx)
-----------------------
2) can be written as Ba&Oa->Dma (by universal specification)
further 2 can be reduced to
3) Ba->(Oa->Dma) (By law of exportation)
4) Oa->Dma (from p->q and p so q)
5) ~Oa (From p&q so q)
So, "we can't conclude that Mary does not date Adams".

Am i wrong? If I'm please explian me where it went wrong. Thanks in advance.

It seems to me that your conclusion is wrong. I am not up on predicate logic, so can't point out where you are going wrong. To belong to the set of boys whom Mary dates, a boy must own a car. Adams doesn't own a car, so he is not a member of that set. The conclusion is that Mary doesn't date Adams.