Which conclusion(s) are correct for the statements?Statements:Some fruits are yellow. All yellow is blue. Some red in blue.Conclusions:I. Some red is yellow.II. Some blue is yellow.III. Some fruits are blue
Question
Which conclusion(s) are correct for the statements?Statements:Some fruits are yellow. All yellow is blue. Some red in blue.Conclusions:I. Some red is yellow.II. Some blue is yellow.III. Some fruits are blue
Solution
To determine the correct conclusion(s) for the given statements, let's analyze each statement and its implications:
Statement 1: "Some fruits are yellow." This statement implies that there exists at least one fruit that is yellow.
Statement 2: "All yellow is blue." This statement implies that everything that is yellow is also blue. However, it is important to note that this statement seems to be logically incorrect, as it contradicts common knowledge.
Statement 3: "Some red in blue." This statement implies that there exists at least one instance where red is present within something that is blue.
Now, let's evaluate each conclusion:
Conclusion I: "Some red is yellow." Based on the given statements, there is no direct connection between red and yellow. Therefore, this conclusion cannot be logically derived from the given statements.
Conclusion II: "Some blue is yellow." Since statement 2 states that all yellow is blue, this conclusion can be logically derived from the given statements.
Conclusion III: "Some fruits are blue." There is no direct connection between fruits and blue in the given statements. Therefore, this conclusion cannot be logically derived from the given statements.
In summary, the correct conclusion(s) for the given statements are:
- Conclusion II: Some blue is yellow.
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