Logic Gates

We are given the logical expression: We need to find the combination of truth values of that makes the above expression false.

Step 1: Understanding the implication.
The logical expression is an implication:
An implication is false only when is true and is false.
Thus, for the expression to be false, we need to have:

Step 2: Checking the conditions.
We need to evaluate both parts of the expression for different combinations of .
Case (1) :
- , since .
- , since .
- , since .
Thus, the expression is true, not false.
Case (2) :
- , since .
- , since and .
- , since and .
Thus, the expression is true, not false.
Case (3) :
- , since .
- , since and .
- , since and .
Thus, the expression is false, as and .
Case (4) :
- , since .
- , since and .
- , since .
Thus, the expression is true, not false.
Step 3: Conclusion.
The combination of truth values that makes the expression false is , which corresponds to option (1).