State whether the following statements are True or False. Give s

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 : 182

a) False. A Hopfield network is a single-layer, fully connected recurrent network in which each neuron is connected to every other neuron (except itself). There are no distinct previous or next layers, and neurons both send and receive signals recurrently. b) False. The length of __________ _______ __________ ______ _____ __________ ______ ___ _____.
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