Read the given statements and conclusions carefully. Assuming that the…
2025
Read the given statements 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 from the statements.
Statements: All chairs are mirrors. Some eagles are mirrors. No mirror is a horse.
Conclusions: (I) No horse is a chair. (II) Some eagles are horses.
- A.
Both conclusions (I) and (II) follow
- B.
Only conclusion (II) follows
- C.
Neither conclusion (I) nor (II) follows
- D.
Only conclusion (I) follows
Attempted by 13 students.
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Correct answer: D
Two syllogism rules govern this pair of conclusions. First, a universal premise ("All A are B") combined with a universal negative premise sharing the middle term ("No B is C") places the entire A category outside the C category, and a universal negative relationship converts simply: "No A is C" and "No C is A" are logically equivalent. Second, a particular premise ("Some A are B") combined with the same universal negative premise only excludes the overlapping part of A from C; it can never be strengthened into a claim that A and C share members.
"All chairs are mirrors" (universal) combined with "No mirror is a horse" (universal negative) places the entire chair category outside the horse category, so no chair is a horse.
A universal negative relationship converts simply, so "no chair is a horse" is logically equivalent to "no horse is a chair" -- exactly what conclusion (I) states, so conclusion (I) follows.
"Some eagles are mirrors" (particular) combined with "No mirror is a horse" (universal negative) can only exclude the overlapping eagles from the horse category; the statements say nothing about the eagles that fall outside the mirror category.
Because a particular-plus-negative pairing can only produce an exclusion result, it cannot be strengthened into a claim that eagles and horses share members -- so conclusion (II), which asserts exactly that, does not follow.
A quick model confirms this: let Mirrors = {1, 2, 3, 4}, Horses = {5, 6} (disjoint from Mirrors, as the third statement requires), Chairs = {1, 2} (a subset of Mirrors, as the first statement requires), and Eagles = {3, 7} (element 3 overlaps Mirrors, satisfying the second statement; element 7 lies outside Mirrors, which the statement allows). In this valid model, no horse is a chair -- confirming conclusion (I) is guaranteed -- while no eagle is a horse at all, showing conclusion (II) is not guaranteed by the statements.
Only conclusion (I) follows from the given statements.