Two dice are tossed. Define the following events. A t: sum of the face values is /, i = 2,3,...,12, B x: difference of the face values is an odd integer, B2: difference of the face values is an even...

Two dice are tossed. Define the following events.

A t: sum of the face values is /, i = 2,3,...,12,

B x: difference of the face values is an odd integer,

B2: difference of the face values is an even integer or 0.

Prove the following.

(a) A t C B\ if i is an even integer.

(b) A t C B2 if i is an odd integer.

(c) A2 U A4U A6 U A8U A 10U A 12= B2.

(d) A x U A3U A5 U A7U A9U A n = B x.