Identify which argument is invalid:
a.) If I catch the bus on time, then I am not late to work.
I was late to work.
Therefore, I did not catch the bus on time.
b.) If I shower in the morning, then I do not smell bad.
I do not smell bad.
Therefore, I showered in the morning.
c.) Either I catch the bus on time or I am late to work.
I did not catch the bus on time.
Therefore, I was late to work.
d.) If the water is filtered, then it will not contain lead.
The water is filtered.
Therefore, it does not contain lead.
e.) If the elephant roars, then it does not want company.
If it does not want company, then it is hungry.
If the elephant roars, then it is hungry.
What do you think? I'll be glad to check your answer.
i think its e.)
Actually, e.) is a valid statement according to the Law of Syllogism.
It's b.)
If I shower in the morning, then I do not smell bad.
I do not smell bad.
You cannot make any valid conclusion because either "I showered in the morning" or "I didn't shower in the morning" makes the first premise true.
p. q. p -> q
T. T. T
F. T. T
The argument that is invalid is e.) If the elephant roars, then it is hungry.
To determine the validity of an argument, we need to examine the logical structure and reasoning. In this case, the argument consists of three conditional statements:
1) If the elephant roars, then it does not want company.
2) If it does not want company, then it is hungry.
3) Therefore, if the elephant roars, then it is hungry.
The issue with this argument is that the conclusion does not necessarily follow from the premises. While it is true that if the first conditional statement is true, it implies the second conditional statement, it does not mean that the conclusion of the argument (if the elephant roars, then it is hungry) is always true.
There could be other factors that cause an elephant to roar, and it does not necessarily mean it is hungry. Therefore, the argument is invalid because the conclusion does not logically follow from the premises.