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Given the following system of axioms

For all A,B,C:

1) A+B=B+A

2) A+(B+C) =(A+B)+C

3) A.B=B.A

4) A.(B.C) = (A.B).C

5) A.(B+C)= A.B+A.C

6) A+0=A

7) A.1=A

8) A+(-A)=1

9) A.(-A)=0

10) A+(BC) = (A+B).(A+C)

11) \(\displaystyle 1\neq 0\)

Then solve the equation :

AX +B =C

Needless to say that since the cancellation law does not work in the above system of axioms ,i have no idea where to even start this problem

For all A,B,C:

1) A+B=B+A

2) A+(B+C) =(A+B)+C

3) A.B=B.A

4) A.(B.C) = (A.B).C

5) A.(B+C)= A.B+A.C

6) A+0=A

7) A.1=A

8) A+(-A)=1

9) A.(-A)=0

10) A+(BC) = (A+B).(A+C)

11) \(\displaystyle 1\neq 0\)

Then solve the equation :

AX +B =C

Needless to say that since the cancellation law does not work in the above system of axioms ,i have no idea where to even start this problem

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