Let P be the predicate defined by P(x,y) = \"x owns y\". Match each English stat

Question

Let P be the predicate defined by P(x,y) = "x owns y".

Match each English statement with the corresponding formal expression that means the same thing.

1.

Jane owns the house Josh doesn't own the cat. (meaningless expression) Everyone owns something. Everything is owned by someone. Some things don't have an owner. Some things are not public property. Some people own nothing. Some people don't own everything. Mr. Burns owns everything. An object cannot have more than one owner. Some people own exactly three things. Some things have more than one owner. There is an object owned by everyone except one person.

1.

.

2.

.

3.

.

4.

.

5.

.

6.

.

7.

.

8.

.

9.

.

10.

.

11.

.

12.

.

13.

.

14.

.

15.

   .

16.

.

Explanation / Answer

A) is matched to 5) as jane owns the house so it is P(jane,house).

B) is matched to 15) as josh doesnt owns a cat , so not P(josh, cat)

C) is matched to 12 ) as it doesnt makes any sense .

D) is matched to 6) as everyone owns something therfore for all x there is something y .

E) is matched to 10) as everythibg us owned by someone i.e. everything has an owner i.e for all y there exist an x

F) is matched ro 2) as for somethings there is no owner.

G) is matched to 3) as few things are nit public property and hence not owned by all x

I)is matched to 14) as some people dont own everything hence there exists a y and an x such that x doesnt own y

H) is matched to 16) as some people own nothing so there exist x such that for all y, x doesnt own y

J) is matched to 8) as mr. Burns owns everything.

K) is matched to 7) as if 2 people own something then they both are same for all things.

L) is matched to 13) as a person exactly owns three things and hence if he owns anything else it is same as those three things

M) is matched to 9) as somethings have more than one owner so y has 2 owners x1 and ×2

N) is matched to 11) as something has all owners except exactly one

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