Get If (condition), then (assign value), else (assign other value) statement in Linear Programming

Question

I'm looking for a linear programming equation that satisfied the conditions;

Given that all variables here are binary variables

if A+B = 2; then C = 1; else C = 0

Also,

if A+B+D = 3; then E = 1; else E = 0

How would one phrase this and satisfy these conditions as well as linearity conditions?

I've tried

A + B - 2 <= M(1-y) and 1 - C <= My

for the first constraint but it doesn't seem to work

Answer 1

For the first equation, you can use:

C + 1 >= A + B
2C <= A + B

If there is a natural sense (max/min) for C in the problem, one of those is sufficient.

Similarly for the second:

E + 2 >= A + B + D
3E <= A + B + D