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 rectangles are trapeziums.
All circles are trapeziums.
Conclusions:
I. Some rectangles being circles is a possibility.
II. Some trapeziums are rectangles.
- AOnly conclusion II follows
- BOnly conclusion I follows
- CBoth conclusions I and II follow
- DNeither conclusion I nor conclusion II follows
Solution & Step-by-step Explanation
Let's analyze the statements:
"All rectangles are trapeziums" → The set of Rectangles is entirely inside the set of Trapeziums.
"All circles are trapeziums" → The set of Circles is also entirely inside the set of Trapeziums.
Now evaluate the conclusions:
Conclusion I: "Some rectangles being circles is a possibility." Since there is no negative constraint bounding rectangles and circles away from each other, they can overlap inside trapeziums. Thus, it is a clear possibility. (Follows)
Conclusion II: "Some trapeziums are rectangles." Since all rectangles are inside trapeziums, that overlapping region means some part of trapeziums is definitively rectangles. (Follows)
Therefore, both conclusions I and II follow.
"All rectangles are trapeziums" → The set of Rectangles is entirely inside the set of Trapeziums.
"All circles are trapeziums" → The set of Circles is also entirely inside the set of Trapeziums.
Now evaluate the conclusions:
Conclusion I: "Some rectangles being circles is a possibility." Since there is no negative constraint bounding rectangles and circles away from each other, they can overlap inside trapeziums. Thus, it is a clear possibility. (Follows)
Conclusion II: "Some trapeziums are rectangles." Since all rectangles are inside trapeziums, that overlapping region means some part of trapeziums is definitively rectangles. (Follows)
Therefore, both conclusions I and II follow.