Do the 2 things respectively with the three syllogistic arguments given below: 1

Question

Do the 2 things respectively with the three syllogistic arguments given below:

1. Translate the following arguments by using predicate letters (as defined below), constant variables, and quantifiers; and

2. Show that they are logically valid by deriving the conclusion from the premises.

{6} [17] P1: All humans have inviolable rights. P2: Not all creatures have inviolable rights. C: Therefore, there are many creatures that cannot be humans. H: being a human I : having inviolable rights C: being a creature

[18] P1: There is no human being who is not mortal. P2: No angels are mortal. C: Therefore, no human beings are angels. H: being a human M: being mortal A: being an angel

Explanation / Answer

Declare the argument to be valid if every starred row has a T in its last column

2. 6.Translate

P1: H -> I

P2: ~C -> I

C: C -> ~H

Let's form the table.

Row 1 indicates it is possible that even when all the premises are true, the conclusion can be false.

Hence, it is INVALID.

18, Translate

P1: ~H -> ~M

P2: ~A -> M

C: ~H->A

Let's form the table.

Declare the argument to be valid if every starred row has a T in its last column.

Hence, it is VALID.

H I C ~C ~H H->I ~C->I C->~H T T T F F T T F T T F T F T T T T F T F F F T F T F F T F F F T F T T F T T T T F T F T T T T T F F T F T T T T F F F T T T F T

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