expectation, probability, Betteley, addition law for expectations

Prove the following addition law for expectations established by Betteley
𝐸(𝑋 𝑉 𝑌) = 𝐸(𝑋) + 𝐸(𝑌) − 𝐸(𝑋 Λ 𝑌)y
Where (𝑋 𝑉 𝑌) = max(𝑋, 𝑌) 𝑎𝑛𝑑 (𝑋 Λ 𝑌) = min(𝑋, 𝑌) and X and Y are two random
variables.
[Hint: the result is analogous to P(A U B) law]