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:
All boxes are squares.
All squares are rectangles.
All rectangles are figures.
Conclusions:
I. All boxes are figures.
II. All squares are figures.

Question

Prepp Team · Accepted Answer

Analyzing Logical Reasoning Statements and Conclusions

This question tests your ability to understand logical deductions based on given statements. We need to determine if the conclusions drawn logically follow from the premises provided.

Understanding the Premises

Let's break down the given statements:

Statement 1: All boxes are squares. This means the set of all boxes is entirely contained within the set of all squares. (Box ⊆ Square)
Statement 2: All squares are rectangles. This means the set of all squares is entirely contained within the set of all rectangles. (Square ⊆ Rectangle)
Statement 3: All rectangles are figures. This means the set of all rectangles is entirely contained within the set of all figures. (Rectangle ⊆ Figure)

Evaluating the Conclusions

We will now check if each conclusion is supported by the statements using the principle of transitivity in logic (If A implies B, and B implies C, then A implies C).

Conclusion I: All boxes are figures.

To check this conclusion, let's combine the statements:

From Statement 1, we know: Box → Square
From Statement 2, we know: Square → Rectangle
From Statement 3, we know: Rectangle → Figure

Combining these, we get a chain: Box → Square → Rectangle → Figure.

Therefore, it logically follows that All boxes are figures. Conclusion I is valid.

Conclusion II: All squares are figures.

To check this conclusion, let's combine the relevant statements:

From Statement 2, we know: Square → Rectangle
From Statement 3, we know: Rectangle → Figure

Combining these, we get a chain: Square → Rectangle → Figure.

Therefore, it logically follows that All squares are figures. Conclusion II is valid.

Summary of Logical Flow

The relationships can be visualized as nested sets:

Boxes

⊂ Squares

⊂ Rectangles

⊂ Figures

This clearly shows that boxes are a subset of squares, squares are a subset of rectangles, and rectangles are a subset of figures. Consequently:

Boxes are within Rectangles, and thus within Figures.
Squares are within Rectangles, and thus within Figures.

Final Decision

Both Conclusion I (All boxes are figures) and Conclusion II (All squares are figures) are logically derived from the given statements.

Prepp Team · Answer

Only conclusion I follows.

Prepp Team · Answer

Only conclusion II follows.

Prepp Team · Answer

Neither conclusion I nor II follows.