If Abe comes to the party, then Bill comes to the party; and if Bill comes to the party, then Carol comes to the party. (A, B, C)

Question

Symbolic Logic , translate single statements, whole arguments, and to use the comparative method to determine validity or invalidity. I have to symbolize these statements by using the Letters provided in the parentheses.

Answer 1

This is an old question, but I am following up on it in case anyone else has a similar one. Maurice's comments are overall correct, but there is a problem. The original question asks you to determine validity.

 

The quality "validity" applies to arguments, not statements. An argument is an arrangement of multiple claims such that one claim is the conclusion and the other claims are the supporting premises. A valid argument is one in which, if the premises are true, then the conclusion cannot be false.

 

The problem, here, is that you don't actually have any conclusion. Not having a conclusion, you don't have an argument. Not having an argument, you have nothing to evaluate as valid or invalid -- the term is meaningless in reference to premises or sets thereof, which is all this is as it stands.

 

In propositional logic, the original sentence could be written two ways; either as a single statement:

 

(A ⊃ B) ∧ (B ⊃ C)

 

... or as two separate statements:

 

(A ⊃ B)

(B ⊃ C)

 

Maurice is correct that these suggest (A ⊃ C), forming what is called the hypothetical syllogism.

 

On your follow-up comment, it is hard to tell what you are asking due to lack of formatting. Trying to decipher it, if you meant to write this,

 

[A . (R v S)] > [L v (E > M)] / [A . (R v S)] // [L v (E > M)]

 

... or this,

 

[A . (R v S)] > [L v (E > M)]

[A . (R v S)]

∴[L v (E > M)]

 

then the form that you have in play is modus ponens.

 

p ⊃ q

p

q

Answer 2

I am not completely sure of the notation required by your teacher, but here is some explanation of what is meant by this question.

Use A to mean 'Abe comes to the party'.

Use B to mean 'Bill comes to the party'.

Use C to mean 'Carol comes to the party'.

Now we can translate the statements above as follows:

If A then B, and if B then C.

From these two statements we can conclude 'if A then C'.

You might have a notation similar to this:

(A>B)U(B>C)>(A>C)

What these arguments mean is that although we don't know whether Abe is coming to the party, we do know that if he does come, we can expect to see Bill and Carol as well.  However, if Abe doesn't come, Bill and Carol, or just Carol, might be there without Abe.