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If the statement 'all students are intelligent' is true, then which of the following statements is/are false?

(i) No students are intelligent.

(ii) Some students are intelligent.

(iii) Some students are not intelligent.

  • a)
    (i) and (ii)

  • b)
    (i) and (iii)

  • c)
    (ii) and (iii)

  • d)
    (i) only

Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the statement all students are intelligent is true, then which of t...

(i) No students are intelligent. → FALSE
(ii) Some students are intelligent. → TRUE, since All students are intelligent.
(iii) Some students are not intelligent. → FALSE, since All students are intelligent.
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Community Answer
If the statement all students are intelligent is true, then which of t...
Understanding the Statements:
The given statement "All students are intelligent" can be represented as follows:
- All Students -> Intelligent

Analysis of the Statements:
(i) No students are intelligent:
This statement contradicts the original statement "All students are intelligent", making it false.
(ii) Some students are intelligent:
This statement is consistent with the original statement and does not contradict it, so it can be true.
(iii) Some students are not intelligent:
This statement contradicts the original statement "All students are intelligent", making it false.

Conclusion:
- Statement (i): No students are intelligent - False
- Statement (ii): Some students are intelligent - True
- Statement (iii): Some students are not intelligent - False

Therefore, the correct answer is option 'B' (i.e., (i) and (iii) are false).
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If the statement all students are intelligent is true, then which of the following statements is/are false?(i) No students are intelligent.(ii) Some students are intelligent.(iii) Some students are not intelligent.a)(i) and (ii)b)(i) and (iii)c)(ii) and (iii)d)(i) onlyCorrect answer is option 'B'. Can you explain this answer?
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