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 conclusions logically follows/follow from the statements. Statements:I. All planets are asteroids.II. All orbits are asteroids.III. No star is an asteroid. Conclusions:I. No planet is a star.II. No star is an orbit.
- AOnly conclusion I follows
- BNeither conclusion I nor II follows
- COnly conclusion II follows
- DBoth conclusions I and II follow
Solution & Step-by-step Explanation
Let's analyze the statements using standard Venn diagrams or logical relations: Statement I: All planets are asteroids. (Planet set is completely inside Asteroid set)Statement II: All orbits are asteroids. (Orbit set is completely inside Asteroid set)Statement III: No star is an asteroid. (Star set is entirely disjoint and separate from Asteroid set)Now let's check the conclusions:Conclusion I: No planet is a star. Since all planets are inside asteroids, and no asteroid can be a star, it is absolutely true that no planet can cross into the star set. Thus, conclusion I follows.Conclusion II: No star is an orbit. Since all orbits are inside asteroids, and no asteroid can be a star, it is absolutely true that no orbit can be a star. Thus, conclusion II follows.Therefore, both conclusions I and II follow.