Consider the following recursively defined set S • Basis elements: {2,4, 8} • Recursive step 1: x, y e S → x * y e S • Recursive step 2: r € S → 2 » T € S Use structural induction to show that all...

Extracted text: Consider the following recursively defined set S • Basis elements: {2,4, 8} • Recursive step 1: x, y e S → x * y e S • Recursive step 2: r € S → 2 » T € S Use structural induction to show that all elements in S are powers of two. Formally, x is a power of two if and only if: 3keN(x = 2*)