Statements: 1. All squares are rectangles. 2. All rectangles are polygons. Conclusions: I. All squares are polygons. II. Some polygons are squares. Which conclusion(s) logically follow? MCQ with Answer and Explanation
Statements:
1. All squares are rectangles.
2. All rectangles are polygons.
Conclusions:
I. All squares are polygons.
II. Some polygons are squares.
Which conclusion(s) logically follow?
A. Only conclusion I follows
B. Only conclusion II follows
C. Neither I nor II follows
D. Both I and II follow
Answer: Option D
Solution (By JKExamLibrary)
A -> B and B -> C means A -> C. Therefore, all squares are polygons (Conclusion I). Since all squares are polygons, it implies that at least some polygons (those specific squares) are squares (Conclusion II).
Statement:
If you work hard, you will succeed in the examination.
Conclusions:
I. Hard work is a sufficient condition for success in the examination.
II. Without hard work, one cannot succeed in the examination.
Which conclusion(s) logically follow?
Explanation:
The statement is an 'If A then B' proposition. It means hard work guarantees success (I follows). However, it does not state 'Only if you work hard', meaning there could be other ways to succeed (e.g., being naturally brilliant). Thus, II does not logically follow.
Statement: Those hilly areas will be declared backward where forest area does not exist.
Conclusions:
I. Hilly forest areas are not backward.
II. In backward areas hills are without forest.
Explanation:
Conclusion I follows: if a hilly area lacks forest, it is declared backward; therefore, hilly areas with forest are not declared backward. Conclusion II does not follow because the statement only defines a condition for declaring backwardness, not that all backward areas are hilly and without forest.
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