Syllogism: Statements and Conclusions — MCQs with Answers (Set 1)

Setting g=1 gives f=1.5, e=3, d=9, c=36, b=108, a=216. Then (a+b+c)=360 and (e-f+g)=2.5, so the ratio is 360/2.5=144.

Statement 1 says all ferries are vessels. Statement 2 says no vessels are aircraft. Chain these using ‘vessels’: ferries sit fully inside vessels, and vessels never touch aircraft. So ferries can never touch aircraft either. This means no ferries are aircraft. This makes conclusion I valid. Statement 3 says some aircraft are gliders. Since no vessels are aircraft, and ferries sit inside vessels, no aircraft can be a ferry either. So the aircraft-that-are-gliders are guaranteed not to be ferries. This means some gliders are not ferries. This makes conclusion II valid too. The correct answer is: both conclusions I and II follow.

Statement 2 says some probes are stations. Statement 3 says all stations are units. Chain these using ‘stations’: the probes that are stations are also units. So some probes are units. This makes conclusion II valid. Now check conclusion I. Statement 1 says all satellites are probes, but satellites are only one part of the whole probe group. The probes that are stations, and later units, may not include any satellites at all. It feels natural to assume satellites inherit the link too, but that link was never actually established. So conclusion I, some satellites are units, is not guaranteed. The correct answer is: only conclusion II follows.

Statement 1 says all bricks are blocks. Statement 2 says no blocks are cushions. Chain these using ‘blocks’: bricks sit fully inside blocks, and blocks never touch cushions. So bricks can never touch cushions either. This means no bricks are cushions. This makes conclusion I valid. Now use statements 2 and 3 together. No blocks are cushions, and all cushions are pillows. So the cushions-that-are-pillows are guaranteed not to be blocks. This means some pillows are not blocks. This makes conclusion II valid too. Each conclusion uses a different pair of statements, but both hold up. The correct answer is: both conclusions I and II follow.

Statement 1 says all turbines are rotors. Statement 2 says all rotors are shafts. Chain these using ‘rotors’: every turbine is a rotor, and every rotor is a shaft. So every turbine must be a shaft. This makes conclusion I valid. Statement 3 says some shafts are couplings. But turbines are only one part of the whole shaft group. The shafts that are couplings may not include any turbines at all. So conclusion II, some couplings are turbines, is not guaranteed. It only follows if the coupling-shafts happen to overlap with turbines, and nothing confirms that. The correct answer is: only conclusion I follows.

Statement 1 says all beams are frames. Statement 2 says all beams are panels. Here ‘beams’ is the shared term, and it is the subject in both statements. Every beam sits inside both frames and panels at the same time. Beams form a real, non-empty group, so frames and panels must overlap through it. So some frames are panels. This makes conclusion I valid. It is tempting to assume no conclusion is possible here, since beams is shared as a subject, not a predicate. That assumption is wrong in this exact case. Conclusion II claims all frames are panels, which is far too strong and unsupported. Many frames could exist outside the beam overlap. The correct answer is: only conclusion I follows.

Statement 1 says all rivets are fasteners. Statement 2 says all bolts are fasteners. Here ‘fasteners’ is the shared term, but it sits as the predicate in both statements. This is different from a chain, and it proves nothing about rivets and bolts directly. Rivets and bolts could be two completely separate groups inside fasteners, with no overlap at all. So conclusion I, some rivets are bolts, is not guaranteed. Conclusion II claims all bolts are rivets, an even stronger, unsupported claim. Both conclusions rely on a connection the statements never actually make. This is a classic trap: sharing one larger category does not link two smaller groups. The correct answer is: neither conclusion I nor II follows.

Statement 1 says some sensors are filters. Statement 2 says some filters are switches. The shared term ‘filters’ is not fully pinned down in either statement. The filters that are sensors, and the filters that are switches, may be completely different filters. So we cannot be sure any sensor is a switch. Conclusion I is not guaranteed true. We also cannot rule out an overlap between sensors and switches either. Conclusion II is not guaranteed true either. But look closely at the two conclusions together. ‘Some sensors are switches’ and ‘no sensors are switches’ are exact opposites. Exactly one of them must be true, even though we cannot tell which. This is the classic ‘either’ situation in syllogism. The correct answer is: either conclusion I or II follows.

Statement 1 says no cartridges are capsules, so these two groups never overlap. Statement 2 says all cartridges are canisters. The shared term is cartridges. Cartridges sit fully inside canisters, and cartridges never touch capsules. So the cartridges-that-are-canisters are guaranteed not to be capsules. This means some canisters are not capsules. This makes conclusion II valid. Conclusion I claims no canisters are capsules at all. This is far stronger. Canisters is a bigger group than cartridges, and other canisters could still be capsules. Conclusion I is not guaranteed and does not follow. The correct answer is: only conclusion II follows.

Statement 1 says all shards are fragments. Statement 2 says some shards are relics. The shared term is shards. Take the shards that are relics. Since all shards are fragments, those same items are also fragments. So those items are both fragments and relics. This means some fragments are relics. This makes conclusion I valid. Conclusion II claims all relics are fragments. Only the shard-relic overlap is confirmed to be fragments. Other relics, outside that overlap, are not accounted for at all. Conclusion II is too strong and does not follow. The correct answer is: only conclusion I follows.

Statement 1 says all lanterns are beacons. Statement 2 says no signals are beacons. The shared term is beacons. Lanterns sit fully inside beacons, and signals never touch beacons at all. So signals can never touch lanterns either. This means no lanterns are signals. This makes conclusion I valid. A statement saying no X are Y always converts safely to no Y are X. So no lanterns are signals also means no signals are lanterns. This makes conclusion II valid too. Both conclusions follow from the statements. The correct answer is: both conclusions I and II follow.

Statement 1 says all harbors are docks. Statement 2 says no docks are lagoons. The shared term is docks. Harbors sit fully inside docks, and docks never touch lagoons. So harbors can never touch lagoons either. This means no harbors are lagoons. This makes conclusion I valid. A statement saying no X are Y always converts safely to no Y are X. So no harbors are lagoons also means no lagoons are harbors. This makes conclusion II valid too. Both conclusions follow from the statements. The correct answer is: both conclusions I and II follow.

Statement 1 says some spindles are cylinders. Statement 2 says no cylinders are tubes. The shared term is cylinders. Take the spindles that are cylinders. Since no cylinders are tubes, those same spindles cannot be tubes either. So some spindles are not tubes. This makes conclusion II valid. Conclusion I claims no spindles are tubes at all. This is a much stronger claim. Other spindles, outside the cylinder overlap, could still be tubes for all we know. Conclusion I is not guaranteed and does not follow. The correct answer is: only conclusion II follows.

Statement 1 says all granules are particles. Statement 2 says some particles are crystals. The shared term ‘particles’ is not fully pinned down in either statement. We only know granules sit somewhere inside particles. We only know some particles, not necessarily the granule ones, are crystals. The crystal-particles could easily be a completely different set from the granules. So conclusion I, some granules are crystals, is not guaranteed. Conclusion II says the same thing in reverse, so it fails for the same reason. Neither conclusion is forced true by the statements. The correct answer is: neither conclusion I nor II follows.

Statement 1 says no pebbles are stones, so the two groups never overlap. Statement 2 says all stones are rocks. The shared term is stones. Stones sit fully inside rocks, and stones never touch pebbles. So the stones-that-are-rocks are guaranteed not to be pebbles. This means some rocks are not pebbles. This makes conclusion II valid. Conclusion I claims no pebbles are rocks. This is too strong. Rocks is a much bigger group than stones, and pebbles could still overlap with rocks through some other, non-stone path. Conclusion I is not guaranteed and does not follow. The correct answer is: only conclusion II follows.

Statement 1 says some ribbons are threads. Statement 2 says all threads are fibers. The shared term is threads. Take the ribbons that are threads. Since all threads are fibers, those same ribbons are also fibers. So some ribbons are fibers. This makes conclusion I valid. Conclusion II claims all ribbons are fibers. Only the ribbon-thread overlap is confirmed to be fibers. Other ribbons, outside that overlap, are not accounted for at all. Conclusion II is too strong and does not follow. The correct answer is: only conclusion I follows.

Statement 1 says all coils are conductors. Statement 2 says all coils are components. Here ‘coils’ is the shared term, and it is the subject in both statements. Every coil sits inside both conductors and components at once. Coils form a real, non-empty group, so this overlap between conductors and components must exist. So some conductors are components. This makes conclusion I valid. Conclusion II claims all conductors are components. Nothing tells us about conductors outside the coil group. Many conductors could exist that are not components at all. Conclusion II is too strong and does not follow. The correct answer is: only conclusion I follows.

Statement 1 says all valves are pumps. Statement 2 says all pumps are engines. Chain these using the shared term pumps. Every valve is a pump, and every pump is an engine. So every valve is also an engine. This means valves sit inside engines, not outside them. Conclusion I claims all engines are valves. This reverses the chain illegally and does not follow. Conclusion II claims no engines are valves. But we just showed valves are inside engines, so some engines must be valves. Conclusion II directly contradicts this and does not follow either. The correct answer is: neither conclusion I nor II follows.

Statement 1 says all prisms are solids. Statement 2 says all solids are objects. Chain these using the shared term solids. Every prism is a solid, and every solid is an object. So every prism is also an object. Prisms form a real, non-empty group inside objects. So some objects must be prisms. This makes conclusion II valid. Conclusion I claims some objects are not prisms. Nothing in the statements guarantees this. Objects could, in principle, contain only prisms and nothing else. So conclusion I is not guaranteed and does not follow. The correct answer is: only conclusion II follows.

Statement 1 says all ledgers are folders. Statement 2 says all folders are archives. Chain these using the shared term folders. Every ledger is a folder, and every folder is an archive. So every ledger must be an archive. This makes conclusion I valid. Conclusion II reverses the last statement and claims all archives are ledgers. This is illicit conversion, a classic error. All folders are archives never means all archives are folders. Archives is the larger group here, so it can hold many non-ledgers. Conclusion II does not follow. The correct answer is: only conclusion I follows.

Statement 1 says all modules are circuits. Statement 2 says all circuits are devices. Chain the two using the shared term circuits. Every module is a circuit, and every circuit is a device. So every module must be a device. This makes conclusion I valid. Modules form a real, non-empty group inside devices. So at least some devices must be modules. This makes conclusion II valid too. Both conclusions follow from the statements. The correct answer is: both conclusions I and II follow.