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Consider the following three statements:
(i) Some roses are red.
(ii) All red flowers fade quickly.
(iii) Some roses fade quickly.
Q. Which of the following statements can be logically inferred from the above statements?
- a)If (i) is true and (ii) is false, then (iii) is false.
- b)If (i) is true and (ii) is false, then (iii) is true.
- c)If (i) and (ii) are true, then (iii) is true.
- d)If (i) and (ii) are false, then (iii) is false.
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Consider the following three statements:(i) Some roses are red.(ii) Al...
Given statements:
(i) Some roses are red.
(ii) All red flowers fade quickly.
(iii) Some roses fade quickly.
Explanation:
To determine which statements can be logically inferred from the given statements, we need to analyze the relationships and implications between them.
Statement (i): Some roses are red.
This statement implies that there exists at least one rose that is red. It does not provide any information about other roses or flowers.
Statement (ii): All red flowers fade quickly.
This statement implies that every red flower fades quickly. It does not provide any information about roses that are not red or about roses in general.
Statement (iii): Some roses fade quickly.
This statement implies that there exists at least one rose that fades quickly. It does not provide any information about the color of the roses or about other flowers.
Logical Inferences:
Based on the given statements, we can make the following logical inferences:
Inference 1: If (i) is true and (ii) is true, then (iii) is true.
If there exists at least one rose that is red (i) and all red flowers fade quickly (ii), then it is implied that there exists at least one rose that fades quickly (iii). This inference is valid because the conditions in (i) and (ii) are fulfilled.
Inference 2: If (i) is true and (ii) is false, then (iii) is true.
If there exists at least one rose that is red (i) and not all red flowers fade quickly (ii), then it is still possible for there to exist at least one rose that fades quickly (iii). This inference is valid because the conditions in (i) are fulfilled, and the condition in (ii) does not contradict the possibility of (iii).
Inference 3: If (i) is false and (ii) is true, then (iii) is false.
If there are no roses that are red (i) and all red flowers fade quickly (ii), then it is not possible for there to exist any rose that fades quickly (iii). This inference is valid because the condition in (ii) implies that only red flowers fade quickly, and if there are no red roses, then there are no roses that fade quickly.
Inference 4: If (i) is false and (ii) is false, then (iii) is false.
If there are no roses that are red (i) and not all red flowers fade quickly (ii), then it is not possible for there to exist any rose that fades quickly (iii). This inference is valid because the condition in (ii) does not imply that all roses fade quickly, and the condition in (i) implies that there are no red roses.
Conclusion:
Based on the logical inferences, we can conclude that if both (i) and (ii) are true, then (iii) is true. Hence, option 'C' is the correct answer.
(i) Some roses are red.
(ii) All red flowers fade quickly.
(iii) Some roses fade quickly.
Explanation:
To determine which statements can be logically inferred from the given statements, we need to analyze the relationships and implications between them.
Statement (i): Some roses are red.
This statement implies that there exists at least one rose that is red. It does not provide any information about other roses or flowers.
Statement (ii): All red flowers fade quickly.
This statement implies that every red flower fades quickly. It does not provide any information about roses that are not red or about roses in general.
Statement (iii): Some roses fade quickly.
This statement implies that there exists at least one rose that fades quickly. It does not provide any information about the color of the roses or about other flowers.
Logical Inferences:
Based on the given statements, we can make the following logical inferences:
Inference 1: If (i) is true and (ii) is true, then (iii) is true.
If there exists at least one rose that is red (i) and all red flowers fade quickly (ii), then it is implied that there exists at least one rose that fades quickly (iii). This inference is valid because the conditions in (i) and (ii) are fulfilled.
Inference 2: If (i) is true and (ii) is false, then (iii) is true.
If there exists at least one rose that is red (i) and not all red flowers fade quickly (ii), then it is still possible for there to exist at least one rose that fades quickly (iii). This inference is valid because the conditions in (i) are fulfilled, and the condition in (ii) does not contradict the possibility of (iii).
Inference 3: If (i) is false and (ii) is true, then (iii) is false.
If there are no roses that are red (i) and all red flowers fade quickly (ii), then it is not possible for there to exist any rose that fades quickly (iii). This inference is valid because the condition in (ii) implies that only red flowers fade quickly, and if there are no red roses, then there are no roses that fade quickly.
Inference 4: If (i) is false and (ii) is false, then (iii) is false.
If there are no roses that are red (i) and not all red flowers fade quickly (ii), then it is not possible for there to exist any rose that fades quickly (iii). This inference is valid because the condition in (ii) does not imply that all roses fade quickly, and the condition in (i) implies that there are no red roses.
Conclusion:
Based on the logical inferences, we can conclude that if both (i) and (ii) are true, then (iii) is true. Hence, option 'C' is the correct answer.
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Community Answer
Consider the following three statements:(i) Some roses are red.(ii) Al...
Consider the following Venn diagram:
If all red flowers fade quickly and some roses are red, then these roses being red flowers will also fade quickly.
Hence, it can be inferred that some rose fade quickly if the statements (i) and (ii) are true.
Whereas if any of the statements (i) and (ii) are false, nothing can be inferred about statement (iii).
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Consider the following three statements:(i) Some roses are red.(ii) All red flowers fade quickly.(iii) Some roses fade quickly.Q. Which of the following statements can be logically inferred from the above statements?a)If (i) is true and (ii) is false, then (iii) is false.b)If (i) is true and (ii) is false, then (iii) is true.c)If (i) and (ii) are true, then (iii) is true.d)If (i) and (ii) are false, then (iii) is false.Correct answer is option 'C'. Can you explain this answer?
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