2. Which of the following can only be used in disproving the statements?a) Direct proofb) Contrapositive proofsc) Counter Exampled) Mathematical Induction

Answering the Question

To determine which option can only be used in disproving statements, let's analyze each choice:

1. Direct Proof: This method establishes the truth of a statement by deriving it from axioms, definitions, and previously established theorems. It cannot be used to disprove statements.

2. Contrapositive Proof: This approach involves proving the contrapositive of a statement, which is logically equivalent to the original statement. Thus, it is also used for proving, not disproving.

3. Counter Example: This method specifically provides an example that contradicts a statement, effectively demonstrating that the statement is false. This is the primary technique used for disproving statements.

4. Mathematical Induction: This is a proof technique used to establish the truth of an infinite number of statements, particularly those indexed by the natural numbers. It is a method of proof rather than disproof.

Conclusion

The correct option that can only be used in disproving statements is c) Counter Example.