Let E1 and E2 be two events in the space ????. The following are some proper-ties of the probability measure P. Prove the following:If E1 and E2 are two events in ???? and P is a probability measure, then P is a monotonic function, that is, i. PE()12≤PE(),ifE1E2⊂

ii. P(E1c ) = 1− P(E1 )

iii. PE(1)+=PE(2)PE()12∪E+P()E12∩E iv. P(E1 ∪E2 ) = P(E1 )+ P(E2 )− P(E1 ∩E2 )