Determine whether the statement (3) follows from statement (1) and (2) by the law of detachment or the law of syllogism. If it does, state which law was used. If it does not, write invalid.
(1) if you study you will be smart
(2) if you are smart you will win the spelling bee
(3) if you study math you will win the spelling bee
Select one
A. Invalid
B. Yes, law of syllogism
C. Yes law of detachment
I believe it is A. Invalid
I agree. It looks like a syllogism, but there are too many things wrong.
To determine whether statement (3) follows from statement (1) and (2) using the law of detachment or the law of syllogism, we need to examine the logical connections between the statements.
The law of detachment states that if we have a conditional statement (if p, then q) and we have the premise (p) as true, then we can conclude the conclusion (q).
The law of syllogism states that if we have two conditional statements (if p, then q) and (if q, then r), we can conclude the conclusion (r).
Let's analyze the given statements:
(1) if you study, you will be smart
(2) if you are smart, you will win the spelling bee
(3) if you study math, you will win the spelling bee
To apply the law of detachment or the law of syllogism, we need to find a direct logical connection between the statements. In this case, we notice that there is no direct connection between studying math and winning the spelling bee in the given statements (1) and (2). Thus, we cannot apply either the law of detachment or the law of syllogism to derive statement (3) from (1) and (2).
Therefore, the correct answer is A. Invalid.