Find simple expressions for the following eventsSolutionaEUE

Find simple expressions for the following events.

Solution

a)EUE^c=S--universal set

b)EE^C=?-null set

c)(EUF)(EUF^c)=((EUF)E)U(EUF)F^c = EU(EF^c)=(EUE)(EF^c)=EF^c=E-(EF)

d)(EUF)(E^cUF)(EUF^c)=(EUF)(EUF^c)(E^cUF)=(EF^c)(E^cUF)=EE^cF^cUEFF^c=?U?=?---null set

e)(EUF)(FUG)=((EUF)F)U((EUF)G)=FU(EGUFG)=FU(EUF)G=(EUF)G