Read the given statement(s) 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 statement(s).
Statements: Some mirrors are angles. All ellipses are angles.
Conclusions (I): Some ellipses are mirrors
Conclusions (II): All angles are ellipses
Read the given statement(s) 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 statement(s).
Statements: Some mirrors are angles. All ellipses are angles.
Conclusions (I): Some ellipses are mirrors
Conclusions (II): All angles are ellipses
Solution
- Statement I: Some mirrors are angles. This indicates an overlap between the set of mirrors and the set of angles.
- Statement II: All ellipses are angles. This means the entire set of ellipses is a subset of the set of angles.
Conclusion (I): Some ellipses are mirrors. This does not logically follow. While both mirrors and ellipses are related to angles, there's no information to suggest an overlap between ellipses and mirrors. Ellipses could be a subset of angles that does not intersect with the portion of angles that are mirrors.
Conclusion (II): All angles are ellipses. This is the converse of Statement II and is not necessarily true. If all ellipses are angles, it does not imply that every angle must be an ellipse. There can be angles that are not ellipses (e.g., those angles that are mirrors but not ellipses).