You don't need to diagram the statements out to find the correct answer here. But I have diagrammed them for you below just in case you were curious:
"People are not happy unless they feel that they are needed by others."
So: if people are happy, then they feel that they are needed by others.
P1: PH ==> FNBO not FNBO ==> not PH
"Most people in modern society can achieve a feeling of indispensability only within the sphere of family and friendship."
Q1: PMS-most-FIOFF FIOFF-some-PMS
"almost everyone knows that his or her job could be done by any one of thousands of others."
So: Most people know that his or her job could be done by any one of thousands of others
Q2: PK-most-JDA JDA-some-PK
Now, we are told that a required condition, i.e. the necessary condition, for people being happy is that they feel needed by others. We also know that the majority of people only feel indispensable, i.e. only feel needed, within the sphere of family and friendship. Remember that a majority, i.e. most, means more than 50%, but less than 100%. So, this means that at least one person does feel indispensable outside of the sphere of family and friendship, i.e. answer choice (E): "Fewer than a majority (some) of people in modern society can find happiness outside the sphere of private interpersonal relationships."
Hope that helps! Please let us know if you have any other questions.
