I would like to conduct a little test on the giantbomb community. I would like to ask five questions pertaining to the structure of logical argument. These questions will be ever increasing in difficulty, with the first questions being the easiest and the finally question being the most difficult. All the questions will include the use of basic symbolic notation  
-> condition symbol (If you come with me THEN I'll go to the store)
^ and  (Jack AND Jill went up the hill)
~ not (ex: it is NOT the case that anything will happen)
.:. therefore (conclusion) 
P.Q.R.S..... argument premises   
 
Most of the questions will not require a knowledge of symbolic notation as they should be logically self evident. Please DM me your answer as to allow other members to participate as well. Each line in the presented arguments is a premise in a symbolized argument and the line with the .:. is the arguments conclusion.Your job is to look at the conclusion and see if you could derive that conclusion from the premises before it. Please feel free to ask any questions in the comment section. 
 
 
Question 1) Is the following argument logically sound? (is it valid) 
 
 P-> Q 
Q->R 
.:. P->R
 
The argument is a serise of conditionals. if it were presented as a worded argument is would look like this 
 If P: Jack is at home ->:then Q: it is 6:00pm 
If Q: it is 6:00pm ->then R: Jack's mother is cooking. 
.:. therefore if P: Jack is at home ->then R: Jack's mother is cooking 
 
However the P. Q. R could be any premise in an argument