Statements:
(I) Some books are erasers.
(II) Some erasers are black.
(III) No black is green.
Conclusions:
(I) Some books are green.
(II) All erasers are green.
Which of the following conclusions can be definitely drawn from the given statements?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Neither (I) nor (II) follows
A conclusion follows only if it is true in every diagram that fits the statements.
“Some books are erasers”: the circles of books and erasers overlap
“Some erasers are black”: the circles of erasers and black overlap
“No black is green”: the circles of black and green do not touch; nothing is said about green and the other two
Conclusion (I) (Some books are green) does not follow: the green circle can be drawn away from the books circle, as above, and that diagram still fits all three statements.
Conclusion (II) (All erasers are green) does not follow: some erasers are black, and no black is green, so those erasers are not green (the shaded part).