Question

Each question consists of a set of numbered statements. Assume that each one of these statements is individually true. Each of the four choices consists of a subset of these statements. Choose the subset as your answer where the statements therein are logically consistent among themselves.
A. If Kumar sings, then the audience sleeps.
B. If Kumar sings, then the audience dances.
C. Unless the audience does not dance, the concert will be successful.
D. Only if the audience dances, will the concert be successful.
E. If Vina dances, then Kumar sings.
F. Kumar sings only if Vina dances.
G. Vina dances.
H. The concert is successful.

• A. C, F, G, B and H
• B. A, C, F, G and H
• C. E, C, G, B and H
• D. Both (2) and (3)

Hint:

Only E gives “Vina dances implies Kumar sings” in the useful direction; F runs the other way and cannot pin down whether Kumar sang.

Answer 1

The Correct Option is C

Translate each line into an if-then rule using k = Kumar sings, d = audience dances, s = audience sleeps, v = Vina dances, c = concert successful. A: k → s. B: k → d. C: d → c (unless the audience does not dance, it is successful, meaning if the audience does dance, it is successful). D: c → d. E: v → k. F: k → v. G: v is true. H: c is true.

1. Option 1 (C, F, G, B, H): G gives v = true. F only tells us what follows if Kumar sings (k → v), and since v is already true this rule gives no new information about k, so k stays undecided from this subset. With k undecided, B (k → d) cannot pin down d, and C (d → c) then cannot be used to confirm H. The subset asserts H as a fact but cannot connect it to G through the rules given, so it does not form one linked, checkable chain.
2. Option 2 (A, C, F, G, H): The same problem as above remains, since F still cannot fix k from v = true, so k, d and the sleeping fact from A are all left hanging with no way to reach or confirm H. Rule A also introduces the idea of sleep, which none of the other rules in this subset connect back to dancing or success, adding an unused, dangling fact rather than closing the chain.
3. Option 3 (E, C, G, B, H): G gives v = true. Rule E (v → k) now directly forces k = true, since its condition is met. Rule B (k → d) then forces d = true. Rule C (d → c) then forces c = true, which matches H exactly. Every fact in this subset is reached by a clean, unbroken chain from G all the way to H.

Since option 2 fails and option 3 succeeds, option 4 (claiming both 2 and 3 hold) is also wrong.

So the correct answer is option 3, E, C, G, B and H.