Identify which argument is invalid.
If Sandra pays all of her taxes on time, then she will not incur a penalty.
Sandra did not incur a penalty.
Therefore, she paid all her taxes on time.

If Gene does not do the dishes, then he will play tennis.
If he plays tennis, he will get thirsty.
Therefore, if Gene does not do the dishes, then he will get thirsty.

If Sandra pays all of her taxes on time, then she will not incur a penalty.
Sandra paid all her taxes on time.
Therefore, she did not incur a penalty.

Either Jan is lost, or Jan needs a map.

Question

Identify which argument is invalid. 
       If Sandra pays all of her taxes on time, then she will not incur a penalty. 
Sandra did not incur a penalty.
Therefore, she paid all her taxes on time. 

       If Gene does not do the dishes, then he will play tennis. 
If he plays tennis, he will get thirsty. 
Therefore, if Gene does not do the dishes, then he will get thirsty.  

       If Sandra pays all of her taxes on time, then she will not incur a penalty. 
Sandra paid all her taxes on time. 
Therefore, she did not incur a penalty. 

       Either Jan is lost, or Jan needs a map.

anonymous · Answer

Once more into P and Q land.  I think you should try to do the P and Q stuff by yourself.  However, I will note that for the first case, it is possible that she did not pay all her taxes and time and did not incur a penalty.  And for the last case, Jan definitely needs a map.

anonymous · Answer

on time