Answer to Question #97867 in Discrete Mathematics for jovyshanty

Question

1.In class of 40 students, 38 offer maths, 24 offer English. Each of the students offer at least one of the two subjects. How many students offer both subjects?

2. If A={ 3 ,4 ,5 ,9 and B={1,2,6,9,7}. Find (I) A–B (ii)B n A.

Answer 1

1.In the class 40 students, 24 offer English and each of students offer at least one of the two subjects. It means that $40-24=16$ students offer Maths. But we know that 38 students offer Maths. 16 students are not enough 22 to 38 ($38-16=22$ ). But all other student (expect 16 who offer Maths) offer English. It means 22 students offer 2 subjects.

Answer: 22 students offer both subjects.

2. $A= \{ 3,4,5,9 \},B= \{ 1,2,6,9,7 \}$ .

(I) $A-B$ means that from the set A you need to pick up the common elements between A and B or $A-B= \{ x \in A \mid x \notin B \}$ . The common element between A and B is 9. So $A-B = \{ 3,4,5 \}$.

(II) $B \cap A = \{ x \in A \mid x \in B \}$ or the common elements A and B. It's 9. $B \cap A = \{ 9\}$ .

Answer: $A-B = \{ 3,4,5 \}$ , $B \cap A = \{ 9\}$ .