Question : Directions: Three statements are given, followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All red is pink.
All white is pink.
All pink is orange.
Conclusions:
I. All white is orange.
II. All orange is red.
III. Some oranges are white.
Option 1: Only conclusions I and III follow
Option 2: Only conclusions I and II follow
Option 3: All conclusions follow
Option 4: Only conclusions II and III follow
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Correct Answer: Only conclusions I and III follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion I:
All white is orange – From the above diagram, it is evident that the circle representing white is completely overlapped by the circle representing orange. So, from this, it can be concluded that all white is orange. Therefore, this conclusion follows.
Conclusion II:
All orange is red – From the Venn diagram, it is evident that some parts of the circles representing orange lie outside the circle representing red while some lie inside. So, it can be concluded that some orange is red. Therefore, this conclusion doesn't follow.
Conclusion III:
Some oranges are white – From the Venn diagram, it is evident that some parts of the circles representing orange lie outside the circle representing white while some lie inside. So, it can be concluded that some oranges are white. Therefore, this conclusion follows.
So, only conclusions I and III follow. Hence, the first option is correct.
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