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Step 1 of 3 4.027E In order to prove using switching algebra, switching theorems are used. Switching theorems are given as follows: T1 X+0=X T2 X+1=1 T3 X+X=X T4 T5 X+X'=1 T6 X+Y=Y+X T7 (X+Y)+Z=X+(Y+Z) T7' T8 T8' T9 T11' Step 2 of 3 The function of n-input AND gate with variables can be written as follows, The function of (n+1)-input AND gate with variables can be written as follows, Consider the two inputs of an (n+1)-input AND gate are tied together, let us take n and n+1 input. Then the function can be written as follows, Solving the above function using switching theorems as follows, (According to T7') (According to T3') Thus from equation (1), we can say that n-input AND gate and (n+1)-input AND gate are equal if the two inputs of an (n+1)-input AND gate are tied together. Step 3 of 3 The function of n-input OR gate with variables can be written as follows, (2) The function of (n+1)-input OR gate with variables can be written as follows, Consider the two inputs of an (n+1)-input OR gate are tied together, let us take n and n+1 input. Then the function can be written as follows, Solving the above function using switching theorems as follows, (According to T7) (According to T3) Thus from equation (2), we can say that n-input OR gate and (n+1)-input OR gate are equal if the two inputs of an (n+1)-input AND gate are tied together.