Question

a tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. the letter selected will be recorded as the outcome. consider the following events. event x: the letter selected comes before \e\. event y: the letter selected is found in the word \face\. give the outcomes for each of the following events. if there is more than one element in the set, separate them with commas. (a) event \x or y\: (b) event \x and y\: (c) the complement of the event x:

Explanation:

Step1: Identify elements of event X

The first seven letters of the alphabet are A, B, C, D, E, F, G. Event X has letters before E, so X = {A, B, C, D}.

Step2: Identify elements of event Y

The word "FACE" has the letters F, A, C, E. So Y = {F, A, C, E}.

Step3: Find "X or Y"

The union of two sets X and Y, X ∪ Y, contains all elements that are in X or in Y or in both. So X ∪ Y = {A, B, C, D, E, F}.

Step4: Find "X and Y"

The intersection of two sets X and Y, X ∩ Y, contains all elements that are in both X and Y. So X ∩ Y = {A, C}.

Step5: Find the complement of X

The complement of X, denoted as $\overline{X}$, contains all elements in the sample - space that are not in X. The sample - space S = {A, B, C, D, E, F, G}, so $\overline{X}$ = {E, F, G}.

Answer:

(a) {A, B, C, D, E, F}
(b) {A, C}
(c) {E, F, G}