The converse of this: If you study hard, then your grades will be good.
I think it should be : If your grades are good, then you studied hard. Is this correct?
if you study hard you could score good marks.
Sorry, this is not true.
"If you studied hard, then your grades are good" only guarantees good grades if you studied hard, which means that if you don't get good grades, you didn't study hard.
If you get good grades, it does not mean that you studied hard! It also means that if you didn't study hard, you may get good grades, or you may get bad grades.
Let's summarize this in symbolic logic.
p=you studied hard
q=you get good grades.
For the proposition
p->q implies ~q->~p
We cannot deduce the outcome of the other two cases: ~p, q.
So then my answer should be: If you do not study hard, then your grades will not be good. Right?
Sorry to have written a lot but unrelated to the converse.
Your original proposed answer is correct for a converse.
The converse of
P -> Q is Q -> P but the converse is generally not true.
So your original answer for the converse is correct:
"If your grades are good, then you studied hard."
Let me get this straight. I stated the converse was: If you study hard, then your grades will be good.
I chose to go with: If your grades are good, then you studied hard.
So, is this correct because you really have me confused.
Correct!
Yes, you are correct. The converse of the statement "If you study hard, then your grades will be good" is "If your grades are good, then you studied hard."
To understand why this is the converse, let's break down the original statement:
"If you study hard, then your grades will be good."
- The antecedent is "you study hard," which is the condition or situation that must be true.
- The consequent is "your grades will be good," which is the result or outcome that follows if the antecedent is true.
To find the converse of a conditional statement, you simply switch the positions of the antecedent and the consequent. Therefore, the converse would be:
"If your grades are good, then you studied hard."
In other words, if someone's grades are good, it suggests that they have studied hard. However, it's important to note that the converse does not always hold true. Just because someone has good grades does not necessarily mean they studied hard. There could be other factors contributing to their success, such as natural intelligence or effective studying techniques.