Understanding implicit assumptions is a key skill in logical reasoning questions. An assumption is an unstated premise that is taken for granted or supposed in advance, and which must be true for the given statement to be considered valid or meaningful. We need to carefully analyze the given statement and each assumption to determine which one is implicit.

Statement Analysis: Successful People and Happiness

The statement provided is: "Successful people are happy in life."

This statement establishes a link where success implies happiness. In logical terms, it can be represented as:

$$\text{Successful} \implies \text{Happy}$$

This suggests that being successful is associated with or leads to being happy. We are looking for what the speaker or writer of this statement must believe to be true for the statement itself to hold true.

Assumption 1 Analysis: Unhappy People Are Not Successful

Assumption 1 states: "Those that are unhappy are not successful."

Let's represent this logically:

$$\text{Not Happy} \implies \text{Not Successful}$$

This is the contrapositive of the original statement. If the original statement ("Successful people are happy") is true, then its contrapositive ("Those that are unhappy are not successful") must also be logically true. For example, if "All birds have feathers" is true, then "Anything that does not have feathers is not a bird" must also be true.

However, in the context of these types of reasoning questions, an "implicit assumption" often refers to an unstated underlying premise or belief that serves as a foundation for the statement, rather than a direct logical deduction or an equivalent restatement. While Assumption 1 is a valid logical inference from the statement, it is frequently considered a consequence of the statement rather than an underlying assumption that makes the statement itself possible or valid.

Assumption 2 Analysis: Success Gives Happiness

Assumption 2 states: "Most of the times success in one's endeavours gives happiness."

The original statement asserts that "Successful people are happy in life." For this general observation to be true, there must be a reason or a common trend that connects success to happiness. If success never or rarely led to happiness, it would be difficult to claim that successful people are generally happy.

• This assumption provides the underlying reason or mechanism that explains why successful individuals would experience happiness. It acts as a supporting belief for the main statement.
• The phrase "Most of the times" suggests a general tendency rather than an absolute rule, which is reasonable for an underlying assumption in a general statement about people.

Therefore, for the statement "Successful people are happy in life" to be a valid or meaningful claim, it is implicit that success is generally a source of happiness. This assumption must be true for the statement to hold.

Concluding Which Assumption Is Implicit

Based on our detailed analysis:

• Assumption 2 serves as a crucial underlying belief or premise that explains the relationship described in the original statement. It provides the reason why successful people would be happy.
• Assumption 1, while a logically valid contrapositive, is often treated as a direct inference or an equivalent way of stating the given information, rather than an unstated assumption on which the original statement rests in the context of typical reasoning problems.

Hence, only Assumption 2 is implicit in the statement "Successful people are happy in life."