Determine the contrapositve of each of the following statements: If Mohan is a poet, then he is poor

Answer

To determine the contrapositive of the statement "If Mohan is a poet, then he is poor," we can follow these steps:

### Step 1: Identify the components of the statement
We start by identifying the two parts of the conditional statement:
- Let \( P \) be the statement "Mohan is a poet."
- Let \( Q \) be the statement "He is poor."

### Step 2: Write the original statement in logical form
The original statement can be expressed in logical form as:
\[ P \implies Q \]
This means "If \( P \) is true, then \( Q \) is also true."

### Step 3: Determine the negations of \( P \) and \( Q \)
Next, we need to find the negations of both statements:
- The negation of \( Q \) (He is poor) is "He is not poor," which can be written as \( \neg Q \).
- The negation of \( P \) (Mohan is a poet) is "Mohan is not a poet," which can be written as \( \neg P \).

### Step 4: Write the contrapositive
The contrapositive of the implication \( P \implies Q \) is given by:
\[ \neg Q \implies \neg P \]
This means "If \( Q \) is false, then \( P \) is also false."

### Step 5: Write the contrapositive in words
Substituting back the negated statements, we get:
"If Mohan is not poor, then he is not a poet."

### Final Answer
The contrapositive of the statement "If Mohan is a poet, then he is poor" is:
"If Mohan is not poor, then he is not a poet."

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