text: why is 1+1=1 in booles algebra axiom?   you can save a lot of calculation by simply remembering one sentence: http://mathworld.wolfram.com/booleanring.html . this type of ring is useful in logic because in a logical statement, two true statements yield a true statement when conjuncted or disjuncted and thus the truth function taking statements into their truth value is a homomorphism into this ring.