Reduction: Consider the following reduction from 3-SAT. Given a 3-SAT Instance with variables T1, . . . , Tn and clauses C as follows G, , C,n we transform into a SUBSET SUMI problem 2. For each variable zi we define 24i-2 +2 3i and 4j-2 3i 3. For each clause Cj we define yc,,] -UC.2-UC.3 4. The final instance SUBSET SUM consists of the numbers and the separate target integer s. Part 2: Suppose that the 3-SAT formula is satisfiable. Show that the SUJBSET SUM instance defined above is satisfiable. Hint: It may be helpful to view each number in binary and to view 2#x q as the number q shifted by k bits. Part 2: Suppose that the SUBSET SUM instance is satisfiable. Show that the formula 3-SAT formula is satisfiable. Hint: It may be helpful to start by proving smaller claims e.g., try to prove that in any subset sum solution the set S contains eractly one of yi.0 and Reduction: Consider the following reduction from 3-SAT. Given a 3-SAT Instance with variables T1, . . . , Tn and clauses C as follows G, , C,n we transform into a SUBSET SUMI problem 2. For each variable zi we define 24i-2 +2 3i and 4j-2 3i 3. For each clause Cj we define yc,,] -UC.2-UC.3 4. The final instance SUBSET SUM consists of the numbers and the separate target integer s. Part 2: Suppose that the 3-SAT formula is satisfiable. Show that the SUJBSET SUM instance defined above is satisfiable. Hint: It may be helpful to view each number in binary and to view 2#x q as the number q shifted by k bits. Part 2: Suppose that the SUBSET SUM instance is satisfiable. Show that the formula 3-SAT formula is satisfiable. Hint: It may be helpful to start by proving smaller claims e.g., try to prove that in any subset sum solution the set S contains eractly one of yi.0 and