Question

Shankar and Jwala are both members of a Youth club, though they are not speaking to each other and refuse to work with each other. Chaya, the club president, is appointing members to the fundraising committee, but she has resolved that she will not appoint anyone without his or her explicit consent. Shankar tells Chaya, “I will not consent to appointment on that committee unless I know whether Jwala is to be a member of it.” And Jwala says, “I will not consent to be a member of that committee unless I know whether Shankar will be appointed to it.” If all three of these people stick by these resolutions, then :

• A. Neither of them can be appointed to the committee.
• B. They must either both be appointed or both be left out.
• C. The committee may finally have one of them, both of them, or neither of them as members.
• D. Either one of them can be appointed, but not both.

Answer 1

The Correct Option is D

To solve this problem, we need to understand the logic behind the statements made by Shankar and Jwala.

• Shankar will only consent to join the committee if Jwala's membership is confirmed.
• Jwala will only consent to join the committee if Shankar's membership is confirmed.

This creates a dependency loop: Shankar's decision depends on Jwala's decision, and Jwala's decision depends on Shankar's decision. As a result, they cannot both be appointed unless both are willing to rely on each other’s participation, which contradicts their conditions.

Therefore:

• Shankar cannot consent because Jwala's decision is not first.
• Jwala cannot consent because Shankar's decision is not first.

This means:

• It is impossible for both to consent simultaneously.
• Therefore, either one can be independently appointed, provided the other’s consent is not required.

Thus, the correct conclusion is: Either one of them can be appointed, but not both.