The intersection of the sets is { x | x>7 } this is the set of elements common to B and C.
The union of the sets is { x | x≥3 }
The inverse of B in R is { x | x<3 } and the inverse of C in R is { x | x≤7 }
The set { x | 3≤x≤7 } is the intersection of B and not C (or B and the inverse of C).