Read the following statement carefully and identify the conclusion that follows. Statement: All squares are rectangles. All rectangles are quadrilaterals. Conclusions: I. All squares are quadrilaterals. II. Some quadrilaterals are rectangles.

Correct — C.
Rule: All A are B + All B are C → All A are C.
Rule: All B are C → Some C are B.

I: squares sit inside rectangles, rectangles inside quadrilaterals, so all squares are quadrilaterals ✓
II: all rectangles are quadrilaterals, so some quadrilaterals are rectangles ✓

Both follow → option (c).

Why the others are wrong

• (a)
  Only I follows — Only I drops II, which is the second statement turned round. If every rectangle is a quadrilateral, then some quadrilaterals are rectangles.
• (b)
  Only II follows — Only II drops I, a direct chain: every square is a rectangle and every rectangle is a quadrilateral, so every square is a quadrilateral.
• (d)
  Neither I nor II follows — Neither would mean both conclusions go beyond the statements. I chains the two 'All' statements and II turns the second one round, so both are proved.

Draw the statements as circles: squares inside rectangles, rectangles inside quadrilaterals. A conclusion follows only if it holds in every drawing the statements allow.

The square circle lies inside the quadrilateral circle, which is I. The rectangle circle lies inside the quadrilateral circle too, so the quadrilateral circle contains rectangles, which is II.

Key facts

• All A are B with All B are C gives All A are C.
• All A are B converts to Some B are A, not to All B are A.
• Some A are B converts to Some B are A.

Common traps

• Rejecting II because it is not word for word in the statements
• Turning All rectangles are quadrilaterals into All quadrilaterals are rectangles

No directly related past PYQ was found.