A string that contains only 0s, 1s, and 2s is called a ternary string. (a) Determine the simplified recurrence relation for the number of ternary strings of length that do not have two consecutive Os or two consecutive Is by con- sidering the following cases: (i) Strings that start with 2. (ii) Strings that start with 1. (iii) Strings that start with 0. (iv) Alternate strings that do not contain 2. (b) Determine the initial condition for Question 1(a). (c) Determine the number of ternary string of length seven that do not contain two consecutive Os or two consecutive Is.