5. Consider two consistent cuts whose events are denoted by C1 = C1(1),C1(2), ...,C1(n) and C2 = C2(1),C2(2), ...,C2(n), respectively.

Define a third cut, C3 = C3(1),C3(2), ...,C3(n) that is the maximum of C1 and C2; that is, for every k, C3(k) = later of C1(k) and C2(k).

Define a fourth cut, C4 = C4(1),C4(2), ...,C4(n) that is the minimum of C1 and C2; that is, for every k, C4(k) = earlierof C1(k) and C2(k).

Prove that C3 and C4 are also consistent cuts.