Consider the following pseudo code, where x and y are positive integers.

begin 
    q := 0 
    r := x 
   while r ≥ y do 
      begin 
      r := r - y 
      q := q + 1 
    end 
end

The post condition that needs to be satisfied after the program terminates is

Match the following:

Consider the following C program segment.

while(first <= last) 
{ 
    if (array[middle] < search) 
        first = middle + 1; 
    else if (array[middle] == search) 
              found = TRUE; 
          else last = middle - 1; 
    middle = (first + last)/2; 
}
 if (first > last) notPresent = TRUE; 

The cyclomatic complexity of the program segment is ________.

For any two languages L₁ and L₂ such that L₁ is context-free and L₂ is recursively enumerable but not recursive, which of the following is/are necessarily true?

I. $${\overline L _1}$$ (complement of L₁) is recursive
II. $${\overline L _2}$$ (complement of L₂) is recursive
III. $${\overline L _1}$$ is context-free
IV. $${\overline L _1} \cup {L_2}$$ is recursively enumerable