English · Tenses

“Would” highlights a sense of expectation for the future or from the perspective of an expectation set in the past for some time yet to elapse.

Would is an auxiliary verb - a modal auxiliary verb. We use would mainly to:

talk about the past

talk about the future in the past

express the conditional mood

We also use would for other functions, such as:expressing desire, polite requests and questions, opinion or hope, wish and regret.

a) Will

Explanation: This option is not correct. The sentence would be grammatically incorrect if "will" is used in this context. It doesn't fit the structure of the sentence. 

b) Shall

Explanation: This option is not correct. "Shall" is not suitable in this context. It would not fit grammatically in the sentence. 

c) Would

Explanation: This option is correct. The correct sentence is: "Your friend proved more sympathetic than I expected he would do." In this context, "would" is used to express the idea that your friend was more sympathetic than you anticipated. 

d) Should

Explanation: This option is not correct. "Should" would not be appropriate in this sentence. It would change the meaning and not convey the intended message.