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Step 1 of 5 4.04DP Consider the following axioms that are used to prove theorems and T5' using perfect induction: A2=X=0, then X'=1 A4'=0+0=0 Step 2 of 5 Proof for the theorem T1' using perfect induction method : To prove the theorem involving a single variable X by proving it is true for both X=0 and X=1 as follows, X 0 0.1=0 (According to axioms A5 and A4) 1 1.1=1 Thus, the theorem T1' is proved. Step 3 of 5 Proof for the theorem T2' using perfect induction method To prove the theorem (T2' involving a single variable X by proving it is true for both X=0 and X=1 as follows, X 0 0.0=0 (According to axioms A5 and 1 Thus, the theorem T2' is proved. Step 4 of 5 Proof for the theorem T3' using perfect induction method To prove the theorem involving a single variable X by proving it is true for both X=0 and X=1 as follows, 0 0.0=0 (According to axioms A3 and A4) 1 1.1=1 Thus, the theorem T3' is proved. Step 5 of 5 Proof for the theorem T5' using perfect induction method To prove the theorem involving a single variable X by proving it is true for both X=0 and X=1 as follows, 01 0.1=0 (According to axiom 1 0 Thus, the is proved.