Final answer:
The recurrence relation for the number of ways to tile a stripe of length n, assuming tiles are either of length 1 or 2, is T(n) = T(n-1) + T(n-2). This accounts for the ways of placing either a single tile or a double tile at one end and then tiling the rest of the stripe accordingly. Correct answer is option (a) T(n) = T(n-1) + T(n-2)
Step-by-step explanation:
When finding a recurrence relation for the number of ways to tile a stripe of length n, we must consider the ways to place the tiles. Assuming tiles can either be of length 1 or 2 (which is a common scenario in such problems), the recurrence relation reflects the following logic:
If we place a tile of length 1 on the strip, then we have n-1 length left to tile, which is T(n-1).
If we place a tile of length 2, we have n-2 length left to tile, which is T(n-2).
Since these are two distinct ways to tile the strip, we add them together to form the recurrence relation T(n) = T(n-1) + T(n-2).
This implies that the correct answer is option (a), as each tile configuration depends on the configurations possible for the stripes of length n-1 and n-2.