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.
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. Correct Answer Both conclusions I and III follow
The least possible Venn diagram is:
Conclusions:
I. Some diagonals are polygons. → True (As All polygons are angles and All angles are diagonals → Some diagonals are polygons)
II. All diagonals are decagons. → False (As, there is no definite relation between diagonals and decagons. Hence, false)
III. No polygon is a cone. → True (As All polygons are angles, All angles are diagonals, All cones are cubes and No diagonal is a cube → No polygon is a cone)
IV. Some cubes are angles. → False (As All angles are diagonals and No diagonal is a cube → No cubes are angles)
Hence, both conclusions I and III follow.
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