Question:
Given below are two statements :
Statement I: If 'some students are intelligent' is true, then 'some students are not intelligent' is also true. Statement II: If 'all logicians are mathematician' is true, then 'some non-mathematicians are not logicians' will be true. In the light of the above statements, choose the correct answer from the options given below.
Given below are two statements :
Statement I: If 'some students are intelligent' is true, then 'some students are not intelligent' is also true. Statement II: If 'all logicians are mathematician' is true, then 'some non-mathematicians are not logicians' will be true. In the light of the above statements, choose the correct answer from the options given below.
Statement I: If 'some students are intelligent' is true, then 'some students are not intelligent' is also true. Statement II: If 'all logicians are mathematician' is true, then 'some non-mathematicians are not logicians' will be true. In the light of the above statements, choose the correct answer from the options given below.
Updated On: Dec 30, 2025
- Both Statement I and Statement II are true
- Both Statement I and Statement II are false
- Statement I is true but Statement II is false
- Statement I is false but Statement II is true
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The Correct Option is D
Solution and Explanation
The question involves evaluating the truthfulness of two logical statements. Let's analyze each statement one by one:
Statement I: "If 'some students are intelligent' is true, then 'some students are not intelligent' is also true."
- The statement "Some students are intelligent" indicates the existence of at least one or more students who possess intelligence. Logically, this means there exists a subset of students who are intelligent.
- However, the statement "Some students are not intelligent" does not necessarily follow from the first statement. The two statements are not necessarily related because in logic, "some are" does not imply "some are not."
- Thus, Statement I is false. It wrongly assumes that if some are A, then some must be not A, which is not logically valid without further information on the whole set.
Statement II: "If 'all logicians are mathematicians' is true, then 'some non-mathematicians are not logicians' will be true."
- The statement "All logicians are mathematicians" is true, meaning that every logician is also a mathematician. This forms a subset where logicians are entirely within the set of mathematicians.
- Logically, this implies that anyone who is not a mathematician cannot be a logician because all logicians must be mathematicians.
- Therefore, it is true that "some non-mathematicians are not logicians" because non-mathematicians include individuals who cannot be logicians given the premises.
- Thus, Statement II is true.
To conclude, the correct answer is that "Statement I is false but Statement II is true."
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