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Step 1 of 5 4.02DP Consider the following axioms that are used to prove theorems T2-T5 using perfect induction: A2 X=0, then X'=1 A3 A4 A5 0.1=1.0=0 Step 2 of 5 Proof for the theorem T2 using perfect induction method (T2 X+1=1) : To prove the theorem 2 (T2 X+1=1) involving a single variable X by proving that it is true for both X=0 and X=1 as follows, 0 0+1=1 (According to axioms A3' and A5') 1 1+1=1 Thus, the theorem X+1=1 is proved. Step 3 of 5 Proof for the theorem T3 using perfect induction method (T3 : To prove the theorem 3 (T3 X+X=X) involving a single variable X by proving that it is true for both X=0 and X=1 as follows, X+X=X 0 0+0=0 (According to axioms A3' and A4') 1 1+1=1 Thus, the theorem T3, X+X=X is proved. Step 4 of 5 Proof for the theorem T4 using perfect induction method (T4 : To prove the theorem 4 (T4 involving a single variable X by proving it is true for both X=0 and X=1 as follows, 01 0=0 (According to axioms A2 and A2') Thus, the theorem T4, (X')'=X is proved. Step 5 of 5 Proof for the theorem T5 using perfect induction method (T5 X+X'=1) : To prove the theorem (T5 X+X'=1) involving a single variable X by proving it is true for both X=0 and X=1 as follows, 01 1+0=1 (According to axioms and A5') 1 0 0+1=1 Thus, the theorem T5 X+X'=1 is proved.