The proposition 'Some trees are green' is equivalent to which of the following propositions?
(a) Many trees are green.
(b) Some green things are trees.
(c) Some green things are not non-trees.
(d) Trees are usually green.
Select the correct answer from the options given below:
(a), (b), (c) and (d)
The given proposition is 'Some trees are green' — a particular affirmative (I-type) meaning at least one tree is green. We test which listed statements express the same content.
'Many trees are green' conveys the same particular affirmation that at least some trees are green (a quantity of 'many' still asserts 'some are'), so it agrees with the original. 'Some green things are trees' is the logical converse of an I-proposition; conversion of 'Some S are P' to 'Some P are S' is valid, so it is equivalent. 'Some green things are not non-trees' is obtained by obversion of 'Some green things are trees' (dropping the double negation 'not non-trees' returns 'are trees'), so it too carries the same meaning. 'Trees are usually green' again asserts that green holds for trees in general, agreeing with 'some trees are green'.
Since each of the four restatements preserves the particular affirmative sense of the original, all of them are treated as equivalent, so the complete set is selected.
Correct answer: (a), (b), (c) and (d)
Similar Questions
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LIST I
A. Exceptive proposition
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D. Compound propositon
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Choose the correct answer from the options given below: Match List - I with List - II :
List - I
(Figures of Categorical Syllogism)List - II
(Structure)A. First I. M-P, S-M $\rightarrow$ S-P B. Second II. P-M, S-M $\rightarrow$ S-P C. Third III. M-P, M-S $\rightarrow$ S-P D. Fourth IV. P-M, M-S $\rightarrow$ S-P
Choose the correct answer from the options given below :Match List I with List II
Identify the propositions and match the followings.
LIST I
A. Exceptive proposition
B. Categorical Proposition
C. General Proposition
D. Compound propositon
LIST II
I. Ten is greater than five.
II. If the war is declared then petrol prices will go up.
III. The wicked alone are happy.
IV. All mathematicians are skilled logicians.
Choose the correct answer from the options given below:
