$1.$ Let

$($a$)$ Show a neural network that calculates $.$

$($b$)$ Show a neural network that calculates $.$

$($c$)$ Show a neural network that calculates $.$

$($d$)$ Write down the gradient descent update equations for a network to calculate $.$

$($e$)$ Train such a neural network and show weights and the output for each of

i$.01110101,$

ii$.11011010,$

iii.$10101001,$

iv$.11111111,$