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.