Give the weights for a logistic regression model that can approximate the following logical operations. Assume true is represented as 1, and false as 0. Assume that sigmoid(5) is a close enough approximation to 1, sigmoid(−5) is close enough to 0.

(a) and: x1 ∧ x2

(b) or: x1 ∨ x2

(c) negation: ¬x1

(d) nand: ¬(x1 ∧ x2). Note that nand (not and) is of interest because all Boolean functions can be built using nand.
Use w0 for the bias term (the weight multiplied by 1) and wi is the weight for xi.