Question 7. (5 points) Let X, Y, Z be three strings of respective lengths r, y, z where z y z. Let 1(X, Y) denote the length of the longest prefix common to both X and Y. For example,f X = instagram Y = international Z-internetworking then 1(X, Y) 2, 1(X, Z) 2, and 1(Y,2-6. Suppose that X, Y, and Z are inserted in an initially empty R-way trie, and that the resulting R-way trie has n nodes (including its root). Consider the following statements about these three strings and their R-way trie. I. If n = 1 + z then I(X, Y) = z 2. If n = 1 + z then X = Y and 1(X,Z) = z 3. If n-1+ z + y + z then I(X, Y)-1(X, Z) = 1(Y, Z) = 0 4. n-1+x+y+z-e(x, Y)- (x, z) (Y,z) Choose one of the following about the above statements: 1. Statements 1, 3 and 4 are true, statement 2 is false 2. Statement 1 is true, statements 2, 3, and 4 are false 3. Statement 3 is true, statements 1, 2, and 4 are false . Statements 1 and 3 are true, statements 2 and 4 are false 5. Statements 1, 2, 3, 4 are false