Q1. State whether the following statements are True or False. Give short proof or a counter example in support of your answer.

• (a)) In the Hopfield network, the neurons belonging to the same layer receive input from the neurons of the previous layer and send their value only to the neurons of the next layer. (200 words)
• (b)) The length of chromosomes to determine the maximum value of the set: S={X|0≤x≤4096} is 12. (200 words)
• (c)) The fuzzy relation (R) given below, is an equivalence relation. R = {1 0.6 0 0.2; 0.6 1 0.4 0; 0 0.4 1 0; 0.2 0 0 1} (200 words)
• (d)) The Self Organizing Map (SOM) is a supervised learning technique. (200 words)
• (e)) In a single layer neural network, if ∑n i=1 x₁₁ > 0, then the output is -1. (200 words)

Q7. Approximate the function f(x)=1+cosx for −1≤ x ≤1, by solving 1-2-1network, using Back propagation algorithm. The weighted structure and initial input are as follows: Weighted structures are: [W] = [-0.25, -0.50; -0.40, -0.1] and bias ͵(0) = [0.1] [V] = [0.1, -0.2]and bias ͵ = [0.5] The initial input is 1. Draw the architecture of the model. Perform one iteration.