$3\mathrm{.}10$ a$.$ Use the Hebb rule as described in Section $3\mathrm{.}5\mathrm{.}2$ to find the weight matrix to store the following $($binary$)$ input$-$output pattern pairs: x$(1)=(101)$ y$(1)=(10)$ x$(2)=(01$ y$(2)=(01)$ b$.$ Using the binary step function $($with threshold $0)$ as the activation function for both layers, test the response of your network in both directions on each of the binary training patterns. In each case, when presenting an input pattern to one layer, the initial activation of the other layer is set to zero. c$.$ Using the bipolar step function $($with threshold $0)$ as the activation function for both layers, convert the training patterns to bipolar form and test the network response in both directions again. Initialize activation as in part b$.$ d$.$ Test the response of your network on each of the following noisy versions of the bipolar form of the training patterns. Iterate as required for stability. $($a$)(0-11)($b$)(001)($c$)(100)($d$)(-10-1)($e$)(-100)($f$)(00-1)($g$)(10-1)($h$)(10)($i$)(01)$ e$.$ In which case does the network stabilize to a correct response, in which cases to an incorrect response, and in which cases to an indefinite or indeterminate re$-$ sponse?