Logic Philosophy Using whatever method you wish show that th

Logic Philosophy

Using whatever method you wish, show that the following arguments are not valid:

Specify an interpretation showing that each QL argument below is formally invalid.

     4. 1. (x)(Ax (y)Bxy)

        2. (x)(y)~Bxy

        -------------------

   .: 3. (3x)Ax

    5. 1.(3x)Mx

        2.(3x)(Kx Lx)

        ---------------

     .: 3.(x)(Mx v Lx)

     6. 1. (x)(3y)(~Gx Hxy)

        2. (3x)(y)Hxy

       ---------------------

    .: 3. (x)Gx

Each of the following arguments is invalid. For each argument, supply a refutation by logical analogy.

    7. Since all atoms are divisible and since some things are not atoms, it follows that some things are not divisible.

    8. There is at least one person who votes for every candidate. But no person votes for himself. Therefore, some candidate votes for himself.

Solution

7. Let A = atoms D = divisible T= Things

A is a subset of D

Some things are not atoms can mean that things are atoms as well as non atoms however T can very well be a complete subset of D which would mean that all things are divisible.

Hence A D and T not disjoint with A does not imply that T is not a subset of D.

T D is very much possible and hence all things could be divisible

8 as no person votes for himself the statement that some candidates vote for himself is invalid. Logically let P be the set of persons and C be set of candidate\'s. V be the fn for voting it means for all itemsin C there is a corresponding voter in P which is not the item in C. hence there does not exist any item in C which has the V function tracing back to the same item in C