Question : Directions: Two statements are given followed by two conclusions numbered I and II. 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:
Some blue is yellow.
All yellow is red.
Conclusions:
I. Some blue is red.
II. All red is yellow.
Option 1: Both conclusions I and II follow
Option 2: Neither conclusion I nor II follows
Option 3: Only conclusion I follows
Option 4: Only conclusion II follows
Correct Answer: Only conclusion I follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some blue is red –
From the Venn diagram, it is evident that the circles representing blue and red overlap and have some parts of their area in common. So, it can be concluded that some blue is red. Thus, this conclusion follows.
Conclusion (II):
All red is yellow –
From the Venn diagram, it is evident that some parts of the circle representing red lie inside the circle representing yellow while some lie outside. So, from this, it can be concluded that some red is blue. Thus, this conclusion does not follow.
So, the only conclusion I follows. Hence, the third option is correct.
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