A nor B = not (A or B) . So

false nor false = true

false nor true = false

true nor false = false

true nor true = false

Therefore

1) ¬A = not A

= A nor A

2) A∨B = A or B

= not (A nor B)

= (A nor B) nor (A nor B)

3) A∧B = A and B

= not ((not A) or (not B)) <--- De Morgan's law

= (not A) nor (not B)

= (A nor A) nor (B nor B)

4) A⇒B = not (A and (not B)) <--- A⇒B is false only if A=true and B=false

= (not A) or B <--- De Morgan's law

= not ((not A) nor B)

= not ((A nor A) nor B)

= ((A nor A) nor B) nor ((A nor A) nor B)

A and B are binary adders

not = -ve A=+ and B=-

and = +ve A=+ and B=+

or = either +ve or -ve Either A=+ or B=-

nor= neither A=+ve or B= -ve

I think

nand = either A is + and B is negative or A is negative and B is positive

Check the terminologies.

dd