Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the
statements.
Statements:
All polygons are angles.
All angles are diagonals.
All cones are cubes.
All cubes are decagons.
No diagonal is a cube.
Conclusions:
I. Some diagonals are polygons.
II. All diagonals are decagons.
III. No polygon is a cone.
IV. Some cubes are angles.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. Both conclusions I and III follow.
The least possible Venn Diagram for the given statements is drawn below:
Conclusions:
I. Some diagonals are polygons → True (As all polygons are angles and all angles are diagonals so, some diagonals are polygons.)
II. All diagonals are decagons → False (It is possible but no definite conclusion can be drawn.)
III. No polygon is a cone → True (As all polygons are angles, all angles are diagonals, all cones are cube and no diagonal is a cube so, no polygon is a cone.)
IV. Some cubes are angles → False (All angles are Diagonals and No diagonal is cube so, cube can never have a positive relation with angles)
Hence, Both conclusions I and III follow.