Consider the statement: "If Sheela is happy, then she does not go to work." Which of the following combinations of Sheela's mood and work status is logically impossible if this statement is true?

Introduction / Context:
Logical reasoning questions often use short statements about everyday situations to test understanding of implication. The statement here says that whenever Sheela is happy, she does not go to work. You must decide which of the listed combinations of happiness and work can never happen if the original statement is true. This is a classic test of interpreting an "if then" statement correctly.

Given Data / Assumptions:
- The given logical rule is: if Sheela is happy, then she does not go to work. - Symbolically, let H represent "Sheela is happy" and W represent "Sheela goes to work". The statement is H implies not W. - The options list different possible combinations of H and W being true or false. - We assume the rule is always true, and we look for a combination that would contradict it.

Concept / Approach:
An implication of the form "if H then not W" is false only when H is true but the consequence not W fails, which means W is true. In all other cases, including when H is false, the implication can still be true. Therefore, the only impossible situation under the given rule is the one where Sheela is happy and still goes to work. This approach uses basic truth table reasoning for conditional statements.

Step-by-Step Solution:
Step 1: Translate the sentence "If Sheela is happy, then she does not go to work" into symbolic form H implies not W. Step 2: Recall that an implication fails only when the condition happens but the required result does not. Step 3: Check option a: Sheela is not happy and she goes to work. Here H is false, W is true. When H is false, the rule makes no requirement, so this case is allowed. Step 4: Check option b: Sheela is happy and she does not go to work. Here H is true and W is false, so not W is true. This exactly matches the rule and is allowed. Step 5: Check option c: Sheela is not happy and she does not go to work. H is false, and again no requirement is violated. This situation is possible. Step 6: Check option d: Sheela is happy and she goes to work. Now H is true and W is also true, so not W is false. This contradicts H implies not W. Step 7: Therefore, the combination where Sheela is happy and still goes to work is logically impossible if the original statement is correct.

Verification / Alternative check:
You can also reason using the contrapositive of the rule. H implies not W is logically equivalent to W implies not H. This means that whenever Sheela goes to work, she is not happy. If an option shows Sheela going to work and being happy at the same time, it clearly violates this contrapositive. Option d exactly does that, confirming it as the impossible situation.

Why Other Options Are Wrong:
Sheela is not happy and she goes to work: The rule only specifies what happens when Sheela is happy. When she is not happy, going to work is completely allowed. Sheela is happy and she does not go to work: This is precisely what the rule predicts, so it is a consistent case. Sheela is not happy and she does not go to work: Again, the condition H is false, so the rule does not constrain this situation.

Common Pitfalls:
A frequent misunderstanding is to read "if H then not W" as a two way statement and to conclude that whenever she does not go to work she must be happy. That would be a different, stronger statement. Another error is to assume that if H is false, the rule is violated, which is not correct for a one way implication. Keeping in mind that only the case H true and W true breaks the rule will help you handle many similar logical questions.

Final Answer:
The combination that is logically impossible is Sheela is happy and she goes to work.