In this assignment, you must create a neural network that solves logic operators or colour clustering problems. You must choose one of the two.

TASK#$1$: Logic Operators

Logical gates are the basis of any modern$-$day computer. The device you are using to read this article is using them for certain. One of the great things about these gates is their easy interpretability. Many of these gates are named in plain English, such as the AND, NOT and OR gates. Others are written in less familiarly but are still simple. These logical gates are summarized in the table below

$\backslash$table$[[$Name$,$NOT,AND,NAND,OR$,$NOR,XOR,XNOR$],[$Alg$.$ Expr.,$\backslash$bar $($A$),$AB$,\backslash$bar $($AB$),$A$+$B$,\backslash$bar $($A$+$B$),$Ao$+$B$,,\backslash$bar $($Ao$+$B$)],[$Symbol$,$A$,,$B$^($A$),,,,,,,,,,,,,\backslash$table$[[1]],,,,],[\backslash$table$[[$Truth$],[$Table$]],,$x$,$B$,$A$,$x$,$B$,$A$,$x$,$B$,$A$,$x$,$B$,$A$,$X$,$B$,$A$,$x$,$B$,$A$,$x$],[0,1,0,0,0,0,0,1,,0,0,,0,1,,0,0,,0,1],[,0,0,1,0,0,1,1,,1,1,,1,0,,1,1,,1,0],[,,1,0,0,$I,$0,1,,0,1,,0,0,,0,1,,0,0],[,,,1,1,,1,0,,1,1,,1,0,1,1,0,,1,1]]$

In this task you need to use a neural network to emulate the behaviour of logical gates.

Methodology

You should have a GUI to choose between the logic gates. Once selecting the gate, the system should define the network structure $($perceptron$,$ or multi$-$layer network$).$

Use backpropagation learning algorithm

Give an initial random number for all the weights and biases

Choose the layers activation function.

Use Gradient Descent as training algorithm

You may use SSE or MSE as performance metric

Your GUI should have a graph showing the classification region after training$($implement a cartesian coordinates in java using GUI$)$