Given below are two premises (a and b). From those two premises four…
2017
Given below are two premises (a and b). From those two premises four conclusions (i), (ii), (iii) and (iv) are drawn. Select the code that states the conclusion/conclusions drawn validly (taking the premises singularly or jointly).
Premises :
(a) All bats are mammals.
(b) No birds are bats.
Conclusions :
(i) No birds are mammals.
(ii) Some birds are not mammals.
(iii) No bats are birds.
(iv) All mammals are bats.
Code :
Answer: C. (iii) only — Concept In categorical logic, ‘All A are B’ means that class A is contained in class B, while ‘No C are A’ means that classes C and A do not overlap. A…
- A.
(i) only
- B.
(i) and (ii) only
- C.
(iii) only
- D.
(iii) and (iv) only
Attempted by 4 students.
Show answer & explanation
Correct answer: C
Concept
In categorical logic, ‘All A are B’ means that class A is contained in class B, while ‘No C are A’ means that classes C and A do not overlap. A universal negative statement can be converted: ‘No C are A’ also means ‘No A are C’; a universal affirmative statement cannot be reversed.
The premises do not state a relation between every member of class C and class B, and universal premises alone do not guarantee that class C has any member.
Application
Represent the first premise as Bats ⊆ Mammals.
Represent the second premise as Birds ∩ Bats = ∅. Because disjointness is symmetric, Bats ∩ Birds = ∅; therefore no bats are birds.
‘No birds are mammals’ does not follow. A bird may be a mammal while still not being a bat.
‘Some birds are not mammals’ does not follow because the premises neither establish the existence of birds nor place any existing bird outside the mammal class.
‘All mammals are bats’ is the converse of ‘All bats are mammals’; reversing a universal affirmative statement is invalid.
Cross-check
Use a countermodel: let Bats = {x}, Mammals = {x, y}, and Birds = {y}. Both premises hold, while conclusions (i), (ii), and (iv) are false and conclusion (iii) remains true.
Result
Thus, only conclusion (iii) follows.