Logical Reasoning - Statement and Conclusion - Discussion
Discussion Forum : Statement and Conclusion - Section 3 (Q.No. 42)
Directions to Solve
In each question below is given a statement followed by two conclusions numbered I and II. You have to assume everything in the statement to be true, then consider the two conclusions together and decide which of them logically follows beyond a reasonable doubt from the information given in the statement.
Give answer:
- (A) If only conclusion I follows
- (B) If only conclusion II follows
- (C) If either I or II follows
- (D) If neither I nor II follows and
- (E) If both I and II follow.
42.
Statements: If all players play to their full potential, we will win the match. We have won the match.
Conclusions:
- All players played to their full potential.
- Some players did not play to their full potential.
Answer: Option
Explanation:
The statement asserts that match can be won only if all the players play to their full potential. So, only I follows while II does not.
Discussion:
3 comments Page 1 of 1.
Debasish Chatterjee said:
1 decade ago
The solution to this question is wrong.
If X, then Y does not mean if Y occurs, X has also occured.
If only X then Y, means that if Y occurs, X has also occured.
This is an example of the first type.
If every one plays to their potential, the team wins. This does not mean, that if 9 players play to their potential, we will never win.
If X, then Y does not mean if Y occurs, X has also occured.
If only X then Y, means that if Y occurs, X has also occured.
This is an example of the first type.
If every one plays to their potential, the team wins. This does not mean, that if 9 players play to their potential, we will never win.
Dhaval said:
1 decade ago
Debasish you are right.
Hileamlak said:
5 years ago
I believe the answer is C and here is my explanation.
I will first try to present a mathematical argument and then try to explain it in English.
So say P and Q are two propositions such that p is equivalent to "All players play to their full potential" and Q is equivalent to "we will win the match".
If that is the case, the proposition "If all players play to their full potential, we will win the match. " is mathematically equivalent to saying P=>Q (P implies Q). This doesn't necessarily mean that Q=>P but this is equivalent to the contrapositive which is ~Q=>~P.
When we translate that to plain English here are the few messages we got from that proposition.
1. If all players play to their full potential, we will win the match.
2. If we lose the match all players haven't played to their potential. (the contrapositive) this is because in a game if players prepare and they will win, so if they lose it has to be such that they didn't prepare.
3. Even though not winning means not preparing, not preparing always doesn't mean losing. From the proposition, we can't deduce if the team is going to lose if all of them didn't prepare.
Hence C is a valid answer. The team could have won, either because all of them have prepared well or just because only some of them did, or it could even be none of them prepared and they still won.
I will first try to present a mathematical argument and then try to explain it in English.
So say P and Q are two propositions such that p is equivalent to "All players play to their full potential" and Q is equivalent to "we will win the match".
If that is the case, the proposition "If all players play to their full potential, we will win the match. " is mathematically equivalent to saying P=>Q (P implies Q). This doesn't necessarily mean that Q=>P but this is equivalent to the contrapositive which is ~Q=>~P.
When we translate that to plain English here are the few messages we got from that proposition.
1. If all players play to their full potential, we will win the match.
2. If we lose the match all players haven't played to their potential. (the contrapositive) this is because in a game if players prepare and they will win, so if they lose it has to be such that they didn't prepare.
3. Even though not winning means not preparing, not preparing always doesn't mean losing. From the proposition, we can't deduce if the team is going to lose if all of them didn't prepare.
Hence C is a valid answer. The team could have won, either because all of them have prepared well or just because only some of them did, or it could even be none of them prepared and they still won.
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