Can someone please write out detailed answers for the ff questions:

Exercise 1: Probability Theoryr 1. Consider two events A and B such that P(A|B) = P(B|A}. If P(A U B) = 1 and P[AHB) > 0, show that PM.) :> 1f2. 2. Let C and D be two events. If C C D, show that P[D\\C} = P[D} 13(0). 3. Let E and F be two events. If G is the set of all elements in E or F but not both, show that P[G} = P{E} + P(F) 2P[E D F}