Solution

The correct answer is A, B and C Only

Key Points

• A perceptron can solve boolean functions that are linearly separable. A problem is linearly separable if you can draw a line (or, more generally, a hyperplane) to separate inputs of different classes.
• Here's how it can represent AND, OR, and NOR:
  • AND Operation: Mapping each set of inputs (0,0), (0,1), (1,0), (1,1) can be solved linearly. The points can be separated into two classes, one for outputs that should be 0 and one for outputs that should be 1.
  • OR Operation: Just like the AND operation, the OR operation is also linearly separable. The (0,0) inputs which yield 0 can be separated from (1,0), (0,1), (1,1) inputs that yield 1.
  • NOR Operation: Similar to the OR operation, the NOR operation is also linearly separable. The NOR operation is simply the inverse of the OR operation.
• However, XOR operation is not linearly separable, that is, there is no straight line that can separate the data for 0s and 1s. So, it can't be represented by a single-layer perceptron.
• Whereas a single layer perceptron can represent only linear separable Boolean functions, a multi-layer perceptron or a deeper neural network model can represent more complex lineraly inseperable functions, such as XOR. This is because layers beyond the first can account for inputs from previous layers, allowing for complex decision boundaries beyond a simple straight line.