The proposition 'All leaves are green' is equivalent to which of the following propositions?
(a) No leaves are green
(b) No leaves are non-green
(c) No leaves are in other colour than green
(d) No green is leaf
Select the correct answer from the options given below:
(b) and (c)
The proposition 'All leaves are green' is a universal affirmative asserting that every leaf falls within the class of green things. We must find which statements express exactly the same meaning.
'No leaves are non-green' is the obverse of the original. Saying every leaf is green is logically identical to saying no leaf falls outside the green class, that is, no leaf is non-green. Obversion preserves meaning, so this statement is equivalent.
'No leaves are in other colour than green' says the same thing in different words, if a leaf can be of no colour other than green, then every leaf must be green. This too is equivalent to the original.
'No leaves are green' directly contradicts the original and cannot be equivalent. 'No green is leaf' would exclude leaves from being green, which reverses and denies the original relationship, so it is not equivalent, it is an invalid conversion of an A proposition. Hence only the two statements 'No leaves are non-green' and 'No leaves are in other colour than green' correctly capture the original meaning.
Correct answer: (b) and (c)
Similar Questions
Which of the following statement is logically equivalent to "No birds are mammals"?
Which of the following statements is contrapositive to the following statement - "Some dogs are not aggressive animals"?
Which of the following refers to an attribute of every categorical proposition which is determined by whether the proposition affirms or denies class inclusion?
Which of the following is converse of 'Some S is P'?
The converse of "All cats are mammals" is
In the statement “No dogs are reptiles”, which terms are distributed?
'All Judges are fairminded' is an example of __________ proposition.
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:'All children are not greedy' is an example of which proposition?
The proposition ‘No historians are non-mathematician’ is equivalent to which of the following proposition?
Important Questions from Structure of Categorical Propositions
- Which of the following statements are logically equivalent?
A. All poems are artworks.
B. No non-poems are non-artworks.
C. Some poems are artworks.
D. All non-artworks are non-poems.
Choose the correct answer from the options given below: - In a categorical proposition, the subject and predicate are connected by :
- If the statement "Some animals are not birds" is given as false, which of the following statements can be inferred to be true?
A. All animals are birds.
B. No birds are animals.
C. No animals are birds.
D. Some animals are birds.
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 :Which of the following statement is logically equivalent to "No birds are mammals"?
