Given : a, b ∈ R a * b = max {a, b} and a o b = min {a, b} Let, a, b, c ∈ R Such that a < b < c. ∴ a * (b o c) = a * [min (b, c)] = a * b = max (a, b) = b....(i) Now, a * b = max (a, b) = b a * c = max (a, c) = c ∴ (a * b) o (a * c) = b o c = min (b, c) = b ... (ii) From (i) and (ii) a * (b o c) = (a * b) o (a * c)