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Statement
(i) All A are B
(ii) All A are C (Hi) Some C are D
Based on these statements find out which at the following conclusions are true.
(1) All c can be B
(2) All A are B as well as C.
  • a)
    Only 1 follows
  • b)
    Only 2 follows
  • c)
    Both follows
  • d)
    None follows
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Statement(i) All A are B(ii) All A are C (Hi) Some C are DBased on the...

This is the general diagram. But C can also be inside B. which is a possibility,
∴ both follows (c)
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Statement(i) All A are B(ii) All A are C (Hi) Some C are DBased on the...
Given Statements:
(i) All A are B
(ii) All A are C
(iii) Some C are D

Conclusion 1: All C can be B
Conclusion 2: All A are B as well as C

Explanation:
To check the validity of the given conclusions, we need to analyze the given statements.

Statement (i) All A are B means that all the elements which are A will also be B. So, B is a universal set for A.

Statement (ii) All A are C means that all the elements which are A will also be C. So, C is also a universal set for A.

Statement (iii) Some C are D means at least one element of C is D. So, D is a subset of C.

Conclusion 1: All C can be B
This conclusion is true as per the given statements. If all A are B and all A are C, then all C can be B. This is because A is a subset of both B and C, and B and C may or may not have any elements in common.

Conclusion 2: All A are B as well as C
This conclusion is also true as per the given statements. If all A are B and all A are C, then all the elements of A are present in both B and C. So, we can say that all A are B as well as C.

Hence, both the conclusions follow from the given statements.

Therefore, the correct answer is option (c) Both follows.
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Statement(i) All A are B(ii) All A are C (Hi) Some C are DBased on these statements find out whichat the following conclusions are true.(1) All c can be B(2) All A are B as well as C.a)Only 1 followsb)Only 2 followsc)Both followsd)None followsCorrect answer is option 'C'. Can you explain this answer?
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