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

Step 1: Set up the rules.
Let k = Kumar sings, d = audience dances, v = Vina dances, c = concert is successful. From the statements: E gives v → k, B gives k → d, C gives d → c, G gives v = true, H gives c = true.

Step 2: Chain forward from the one fact we start with.
G tells us v is true. Feed this into E (v → k): since v is true, k must be true too.

Step 3: Continue the chain.
Now that k is true, feed it into B (k → d): since k is true, d must be true.

Step 4: Finish the chain.
Now that d is true, feed it into C (d → c): since d is true, c must be true.

Step 5: Compare with the asserted fact.
H asserts c is true directly, and our chain independently arrived at c = true as well, so nothing in this subset conflicts.

Step 6: Check the losing options.
In the subsets built from F instead of E, the only rule linking to Kumar singing runs the wrong way (k → v, not v → k), so knowing v is true does not let us pin down whether Kumar actually sang, and the chain to H breaks.

Step 7: Final Answer.
Only the subset E, C, G, B and H forms one complete, unbroken chain from the given fact to the asserted conclusion, so option 3 is correct.