ExI $(4Pt)$ : A store is selling the following packages: main item, secondary item, and a toy of your choice. By spinning a wheel, you may get a gift with the package,

Main items: TV$,$ Dish washer, washing machine, and fridge.

Secondary items: Sound system, microwave, and tablet.

Toys: PS$5,$ WII, and Xbox.

Gifts: radio and mixer.

Rami, Joe, Tally, and Karam purchased the following:

Rami: washing machine, microwave, PS$5,$ radio.

Joe: fridge, tablet, WII.

Tally: fridge, microwave, Xbox, mixer.

Karam: TV$,$ Sound system, PS$5.$

Write each of following statements informally and find its truth$-$value.

a$)EE$ an item I such that $AA$ persons $P,P$ chose I.

b$)EE$ a person $P$ and item I such that $AA$ categories $C,P$ chose IinC.

c$)$ EEA person $P$ such that $AA$ gifts $GP$ won $G.$