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Step 1 of 2 4.031E Shannon's expansion theorem is given by, A Variable can hold two values 1 & 0 or we can say true or complementary form and the function can appear any of one form. Shannon's expansion theorem can be proved by perfect induction method as follows, Case 1: When =0 value is substituted in Shannon's expansion theorem, both left hand side(LHS) of the equation and right hand side (RHS) of the equation should be equal. (Since and (Since 0+X=X) Thus the LHS and RHS are equal, and Shannon's expansion theorem is proved. Step 2 of 2 Case2: When =1 value is substituted in Shannon's expansion theorem, both left hand side(LHS) of the equation and right hand side (RHS) of the equation should be equal. (Since and (Since 0+X=X) Thus, the LHS and RHS are equal, and Shannon's expansion theorem is proved.