2021 CSAT — Q10

Locate. This is a pure-logic question (no passage) — the premise set is the anchor, and a conclusion follows only if the premises make it impossible to be false. Render the chain as sets: Radios overlap Mobiles; Mobiles ⊆ Computers; some Computers are Watches.

Test (does-it-follow — chase the watch-link). Both conclusions need a guaranteed bridge to Watches. The only watch-information is the particular “some computers are watches” — it places at least one watch among computers, but says nothing about which computers. The watch-computers can be a slice of the computer set that contains no mobile (and hence no radio). Build that counter-model: watches sit in the non-mobile part of Computers. Every premise holds; yet no mobile is a watch and no radio is a watch.

• C-I “certainly some radios are watches” — refuted by the counter-model. Not forced.
• C-II “certainly some mobiles are watches” — refuted by the same counter-model. Not forced.

Eliminate by anatomy. (a)/(b)/(c) each assert a watch-link that is possible but not necessary — it sounds reasonable but is unsupported, in deductive dress: a “some… are” premise treated as if it pinned down exactly which members overlap. A particular premise that doesn’t name its members can never force a downstream “certainly.” Key: (d).

Premises: Radios ∩ Mobiles ≠ ∅; Mobiles ⊆ Computers; Computers ∩ Watches ≠ ∅. The only watch-link is a PARTICULAR “some computers are watches” — it need not touch any mobile or radio. Counter-model: let the watch-computers be entirely separate computers from the mobiles. Then no mobile and no radio is a watch, yet every premise holds. So C-I (“certainly some radios are watches”) and C-II (“certainly some mobiles are watches”) are each only POSSIBLE, never forced → (d).

Premises: Radios ∩ Mobiles ≠ ∅; Mobiles ⊆ Computers; Computers ∩ Watches ≠ ∅.

The watches enter only through “some computers are watches.” Nothing ties those particular watch-bearing computers to the mobiles or the radios.

• C-I Some radios are watches — counter-model: watch-computers lie outside the mobile (hence outside the radio∩mobile) region. Premises hold; no radio is a watch. Does not follow.
• C-II Some mobiles are watches — same counter-model: no mobile is a watch. Does not follow.

Neither conclusion is entailed.

Answer: (d) Neither Conclusion-I nor Conclusion-II.

The deciding principle: a particular premise (“some X are Y”) that does not specify which X never forces a “certainly” about a different category. “All mobiles are computers” is a clean universal, so it tempts you to feel the watches must reach the mobiles — but the watches are attached to computers in general, and the mobiles are only a sub-slice of computers; the watch-slice and the mobile-slice can be disjoint. On any syllogism, when the bridge to the asked term runs through an unanchored “some,” the honest verdict is “does not follow.” (d).