State whether the following statements are True or False. Give short p

Question

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.
b) The length of chromosomes to determine the maximum value of the set:

$S = \{X \mid 0 \le x \le 4096\}$ is 12.
c) The fuzzy relation (R) given below, is an equivalence relation.

$$R = \begin{bmatrix} 1 & 0.6 & 0 & 0.2 \\ 0.6 & 1 & 0.4 & 0 \\ 0 & 0.4 & 1 & 0 \\ 0.2 & 0 & 0 & 1 \end{bmatrix}$
d) The Self Organizing Map (SOM) is a supervised learning technique.
e) In a single layer neural network, if $\sum_{i=1}^{n} x_i \omega_i > 0$ , then the output is -1.

10 Jan 2026

Answer :

Word Count : 252

a) False. A Hopfield network is a fully connected recurrent network with a single layer of neurons. Each neuron receives inputs from all other neurons in the same layer (except itself) and feeds back to them. There is no notion of previous or next layers, which is a property of _________ _________ _________ ______ _______ ___.
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