B and C are sets of real numbers as follows

Question

B= {x | x>=3}

C={x | x>7}

Answer 1

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).