The question asks us to identify a statement that is logically valid and can be inferred from the given sentences about Rajan and Sajan's project work.

Project Collaboration Inference

In this scenario, Rajan expresses unhappiness because Sajan chose to undertake the project independently. Sajan then clarifies his preference for working alone. We need to determine which of the provided statements is a sound logical inference from these observations about Rajan and Sajan's project.

Understanding Rajan's Unhappiness

Rajan's reaction is crucial for understanding the situation. He was "not happy that Sajan decided to do the project on his own." This strong emotional response from Rajan suggests that his expectation or desire was different from Sajan's independent action. If Rajan was unhappy about Sajan working alone on the project, it implies that he expected or wanted Sajan not to work alone, but rather to work with him on the project. This is a key piece of information for making a logical inference.

Analyzing Logical Validity of Statements

Let's examine each option provided to determine its logical validity based on the information given about Rajan and Sajan's project and their preferences.

Option 1: Rajan's Group Preference

• The statement says, "Rajan has decided to work only in a group."
• While Rajan was unhappy about Sajan working alone, implying he wanted to work with Sajan on this specific project, the text does not provide enough information to infer that Rajan only works in a group in general. His unhappiness is specific to Sajan's choice for this particular project, not a broader declaration about his entire work preference. Therefore, this statement is too broad and cannot be logically inferred from the sentences.

Option 2: Group Formation Wishes

• The statement says, "Rajan and Sajan were formed into a group against their wishes."
• The text explicitly states Sajan "preferred to work independently," which clearly means he did not wish to work in a group for the project. However, Rajan's unhappiness stems from Sajan working alone, indicating Rajan likely did wish to work with Sajan on the project. Since Rajan's wishes were seemingly aligned with working together, the statement that it was "against their wishes" (plural) is incorrect. Thus, this statement is not logically valid.

Option 3: Sajan's Decision to Work Together

• The statement says, "Sajan had decided to give in to Rajan’s request to work with him."
• This directly contradicts the very first sentence of the passage, which states, "Sajan decided to do the project on his own." Furthermore, Sajan explicitly explained "he preferred to work independently." There is no indication that Sajan gave in to any request to work with Rajan; in fact, the opposite is true – he chose to work alone. Therefore, this statement is factually incorrect based on the passage and cannot be inferred.

Option 4: Rajan's Belief in Collaboration

• The statement says, "Rajan had believed that Sajan and he would be working together."
• Rajan's unhappiness ("Rajan was not happy") directly results from Sajan's decision "to do the project on his own." For Rajan to be unhappy about Sajan working alone, it logically implies that Rajan had a prior expectation or belief that they would indeed be collaborating on the project. If Rajan had no such belief or expectation, Sajan's independent work would not cause him unhappiness in this context. This statement perfectly explains Rajan's reaction and is a strong, logical inference from the given sentences regarding their project collaboration.

Conclusion on Project Inference

Based on the detailed analysis of each statement against the provided text, the most logically valid inference is that Rajan had a prior expectation or belief of working together with Sajan on the project. Rajan's unhappiness serves as direct evidence of this unfulfilled expectation regarding their project collaboration.