To check validity of statement we can use which of the following method

Options

A. Using a counter example
B. Contrapositive method
C. Mehtod of contradiction
D. Any one of these

Answer

To check the validity of a statement, we can use several methods. Let's explore these methods step by step.

### Step 1: Counter Example
- **Explanation**: A counterexample is a specific case that disproves a general statement. For instance, if we have the statement "If \( p \) is a prime number, then \( p + 2 \) is also a prime number," we can use a counterexample to check its validity.
- **Example**: Let’s take \( p = 7 \). According to the statement, \( 7 + 2 = 9 \), which is not a prime number. Thus, this counterexample shows that the statement is false.

### Step 2: Contrapositive Method
- **Explanation**: The contrapositive method involves rephrasing a conditional statement. If we have a statement of the form "If \( A \), then \( B \)", the contrapositive is "If not \( B \), then not \( A \)". If the contrapositive is true, then the original statement is also true.
- **Example**: Consider the statement "If \( x \) is odd, then \( x^2 \) is odd." The contrapositive would be "If \( x^2 \) is not odd, then \( x \) is not odd." If we can prove this contrapositive, we can conclude that the original statement is valid.

### Step 3: Method of Contradiction
- **Explanation**: In this method, we assume that the negation of the statement we want to prove is true. If this assumption leads to a contradiction, then the original statement must be true.
- **Example**: Let's consider the statement "√3 is an irrational number." We assume the opposite, that "√3 is a rational number," and show that this leads to a contradiction. If we cannot find a valid rational representation for √3, we conclude that the original statement is true.

### Final Conclusion
- After analyzing the three methods (Counter Example, Contrapositive Method, and Method of Contradiction), we conclude that these are valid approaches to check the validity of a statement. Therefore, the correct answer is option D, which encompasses all these methods.