Consider the following sentences: All benches are beds. No bed is a bulb. Some bulbs are lamps. Which of the following can be inferred? i. Some beds are lamps. ii. Some lamps are beds. A. Only i B. Only ii C. Both i and ii D. Neither i nor ii

GATE 2017 · General Aptitude · Statements Follow · medium

Answer: Neither inference i nor inference ii can be logically deduced from the given statements. The beds-bulbs disjointness blocks any possible link between beds and lamps. Option D is correct.

1. Establish the full set relationships: Bench subset Bed (all benches are beds). Bed INTERSECT Bulb = empty (no bed is a bulb). Bulb INTERSECT Lamp != empty (some bulbs are lamps, so lamps and bulbs share members).
2. Test Inference i: Some beds are lamps: For a bed to be a lamp it would need to be a bulb first (since lamps that we know of are bulbs). But no bed is a bulb. Could a lamp be not-a-bulb? The only information we have about lamps is that SOME bulbs are lamps; we have no information linking lamps to beds at all. We cannot infer any bed is a lamp. Inference i is FALSE.
3. Test Inference ii: Some lamps are beds: Inference ii is the converse of inference i. If no bed is a lamp (which we established in step 2 by the beds-bulbs barrier), then certainly no lamp is a bed either. The relationship is symmetric for set membership: bed intersect lamp = empty implies lamp intersect bed = empty. Inference ii is also FALSE.