State whether the following statements are True or False. Give short proof or a counter example in support of your answer.
 a) The length of chromosomes to determine the maximum value of the set:
 S ={X 0 ≤x ≤ 4096}is 12.
 b) 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.
 c) In a single layer neural network, if x ,0
ω > then the output is −1.
 d) The fuzzy relation (R) given below, is an equivalence relation.

e) The Self Organizing Map (SOM) is a supervised learning technique.

a) False. The length of chromosomes is related to the encoding of values and precision but is not directly determined by the range of values. The length of chromosomes is typically determined based on the required precision and the complexity of the problem. For the given set S = {0 ≤ x ≤ 4096}, the chromosome length can be adjusted based on the required precision, __________ ____ ___ ________ ___ ________ ___.
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