Based on the provided statements, determine which of the conclusions (I and II) logically follow, assuming the relationships declared are correct. Choose your response from the given options.
Statements:
T > L <= U = P > B <= A
Conclusions:
I. U > A
II. P <= A
Correct Answer :
Either conclusion I or conclusion II is logically valid
Solution :
The correct answer is Either conclusion I or conclusion II is logically valid.
Step-by-Step Explanation:
1. Analyze the Given Statements:
We are given the combined inequality statement:
2. Evaluate Conclusion I () and Conclusion II ():
First, observe that . We can substitute with in Conclusion I:
Conclusion I becomes:
Conclusion II is:
Now, let's examine the relationship between and from the main statement:
Since the inequality signs between and are in opposite directions ( and ), no definite relationship can be established between and on their own. Therefore, individually, neither nor is definitely true.
3. Check for Either-Or Condition:
For two conclusions to form an "Either-Or" pair, the following conditions must be met:
1. Both conclusions must individually be uncertain/invalid based on the statement.
2. Both conclusions must compare the same two elements (here, and , where ).
3. The conclusions together must cover all possible mathematical relations between the two variables (, , and ).
Combining (Conclusion I) and (Conclusion II, which means or ), all three possible mathematical outcomes between and are completely covered.
Hence, exactly one of the two conclusions must logically hold true. Therefore, Either conclusion I or conclusion II is logically valid.
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