$4.$ Show that, $"$If it does not rain or it is not foggy, then the sailing race will be held and the life saving demonstration will go on$.$ If the sailing race is held, then the trophy will be awarded. The trophy was not awarded.", implies $"$It rained." $[10]5.$ Which rules of inference are used below $-$ "I am rich or XP$08$ I have to work. I am not rich or I like playing football. Therefore I have to work or I like playing football." $[2]$