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:
All boxes are squares.
All squares are rectangles.
All rectangles are figures.
Conclusions:
I. All boxes are figures.
II. All squares are figures.
- ABoth conclusions I and II follow.
- BOnly conclusion I follows.
- COnly conclusion II follows.
- DNeither conclusion I nor II follows.
Solution & Step-by-step Explanation
Let's model the concentric relations given in the statements:
Boxes ⊂ Squares ⊂ Rectangles ⊂ Figures.
Now evaluate the conclusions:
Conclusion I: All boxes are figures. Since the circle for boxes lies entirely inside the outermost circle of figures, this conclusion is true.
Conclusion II: All squares are figures. Since the circle for squares also lies completely within figures, this conclusion is also true.
Therefore, both conclusions I and II follow.
Boxes ⊂ Squares ⊂ Rectangles ⊂ Figures.
Now evaluate the conclusions:
Conclusion I: All boxes are figures. Since the circle for boxes lies entirely inside the outermost circle of figures, this conclusion is true.
Conclusion II: All squares are figures. Since the circle for squares also lies completely within figures, this conclusion is also true.
Therefore, both conclusions I and II follow.