In this question, three 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 conclusion(s) logically follows/follow from the statements. Statements: All grains are cereals. Some cereals are fruits. No fruit is a vegetable. Conclusions: I. All cereals can be vegetables. II. All grains are fruits.

Correct — B. Draw the statements as regions, then test each conclusion against every arrangement they allow.

The grain circle sits wholly inside the cereal circle. The cereal and fruit circles overlap somewhere. The fruit and vegetable circles are entirely separate.

Conclusion I says all cereals can be vegetables. They cannot: some cereals are fruits, and no fruit is a vegetable, so part of the cereal circle is barred from the vegetable circle in every allowed drawing. It does not follow.

Conclusion II says all grains are fruits. The cereal-fruit overlap is only partial, and nothing forces the grain part of the cereal circle to fall inside it. It does not follow.

Neither conclusion survives — option (b).

Why the others are wrong

• (a)
  Only Conclusion I follows. — Conclusion I fails on the third statement. No fruit is a vegetable, and some cereals are fruits, so those cereals are shut out of the vegetable set.
• (c)
  Only Conclusion II follows. — Some cereals are fruits leaves the grain part of the cereal circle free to sit outside the overlap, so all grains are fruits is never forced.
• (d)
  Both Conclusions I and II follow. — Both fail, and for different reasons. Conclusion I is not merely uncertain but impossible, while Conclusion II is simply not compelled by a partial overlap.

A three-statement syllogism is solved by drawing, not by intuition about food.

Read each statement as a region. All grains are cereals puts one circle inside another. Some cereals are fruits makes two circles overlap without saying where the grains sit. No fruit is a vegetable holds two circles apart.

Then note which kind of conclusion you have. A definite conclusion, such as all grains are fruits, follows only if every allowed drawing shows it. A possibility conclusion, such as all cereals can be vegetables, follows if at least one allowed drawing shows it.

Key facts

• All grains are cereals places the grain circle wholly inside the cereal circle.
• Some cereals are fruits gives an overlap, not containment, so nothing is forced about the grains.
• No fruit is a vegetable makes the fruit and vegetable circles disjoint.
• A can-be conclusion follows if at least one allowed drawing shows it, while a definite conclusion needs every allowed drawing to show it.

Common traps

• Reading all cereals can be vegetables as merely uncertain, without testing whether any drawing allows it
• Carrying real-world knowledge about grains and cereals into the diagram
• Treating some cereals are fruits as though it also fixed where the grains lie

No directly related past PYQ was found.