Question

Let U denote the set of all students in the business college of a certain university. Let A-(xE U | x had taken a course in accounting) B xEUI x had taken a course in economics) C-xEU | x had taken a course in marketing) Write the set that represents each statement. (a) The set of students who have had courses in economics but not courses in marketing or accounting Bn (CUAC) (b) The set of students who have had at least one of the three courses (c) The set of students who have had all three courses O (BUCU A)

Answer 1

Solution :-

Given data:

Let A = {x $\epsilon$ U | x has taken a course in accounting}

B = { x $\epsilon$ U | x has taken a course in economics}

C = {x $\epsilon$ U | x has taken a course in marketing}

(i) :-

The set of students who have taken a course in economics but not a course in either accounting or marketing.

From given data we can represent the above statement as,  $B\cap ( C^{ c} \cup A^{ c } )$.

i.e, Third option is correct answer.

(ii):-

The set of students who have taken at least one course in one of the three subjects.

From given data we can represent the above statement as,  $A \cup B \cup C$.

Here, $A \cup B \cup C = B \cup C \cup A$

i.e, Third option is correct answer.

(iii):-

The set of students who have taken courses in all three subjects.

From given data we can represent the above statement as,  $A \cap B \cap C$.

Here, $A \cap B \cap C = B \cap C \cap A$

i.e, Third option is correct answer.