Assessment

Tick the answer(s). There can be more than one answers In order to recursively define an entity, we need

[40, 20, 3] = [blank_start]40 : [20, 3][blank_end] = [blank_start]40 : 20 : [3][blank_end] = [blank_start]40 : 20 : 3 : [ ][blank_end]

Is the mathematical recursive definition related to programming?

add[2, 4, 10] = [blank_start]add( 2 : [4, 10] )[blank_end] = 2 + [blank_start]add[4, 10][blank_end] = 2 + [blank_start]add( 4 : [10] )[blank_end] = 2 + 4 + [blank_start]add[10][blank_end] = 2 + 4 + [blank_start]add( 10 : [ ] )[blank_end] = [blank_start]2 + 4 + 10 + add[ ][blank_end] = 2 + 4 + 10 = 16

[99, 9] ++ [23, 1] = [blank_start](99 : [9]) ++ [23, 1][blank_end] = 99 : [blank_start]([9] ++ [23, 1])[blank_end] = 99 : [blank_start]((9 : [ ]) ++ [23, 1])[blank_end] = 99 : [blank_start](9 : ([ ] ++ [23, 1]))[blank_end] = 99 : [blank_start](9 : ([23, 1]))[blank_end] = 99 : 9 : [23, 1] = [99, 9, 23, 1]

Can we prove the property by induction?

What are the orders to prove them? 1) Replace the statement with [blank_start]the base case of Lists[blank_end] 2) Prove the replaced statement using [blank_start]the properties given[blank_end] 3) Replace the statement with [blank_start]the step case of Lists[blank_end] 4) Prove the replaced statement using [blank_start]the properties given[blank_end] 5) Make us of [blank_start]the induction hypothesis[blank_end]