How to correctly create a neural network model and select coefficients for classifying binary features?

Question

Neural networks

Please help me figure out how to create a neural network model (namely architecture) and determine the coefficients for weights.

I have such a problem: It is

necessary to build a network model with direct signal propagation (which is feed-forward) and makes a classification.

The sigmoid ( 1/1+e^-x) is used as an activation function in all neurons.
The object is described by four binary features A , B , C and D (taking the value 0 or 1) features.
And the three classes are X , Y , Z
And the conditions are as follows:
If input A is set to 1, and the rest of the inputs are 0, then this is an object of class X. For an object of class Y, any three inputs must be ones. And for an object of class Z, the values ​​on the pairs of inputs A and C, B and D must not match.