A and B are two sets such that n(A-B)= 14+x , n(B-A)=3x and n(A intersection B)=x and if n(A)=n(B) find x and n(AUB)

Open in App

Solution

$We know that for two sets A and B, n (A - B) = n (A) - n (A \cap B) and n (B - A) = n (B) - n (A \cap B) Now, it is given that n (A - B) = 14 + x; n (B - A) = 3 x and n (A \cap B) = x Therefore, n (A - B) = n (A) - n (A \cap B) \Rightarrow 14 + x = n (A) - x \Rightarrow n (A) = 14 + 2 x . . . . . . . (1) Also, n (B - A) = n (B) - n (A \cap B) \Rightarrow 3 x = n (B) - x \Rightarrow n (B) = 4 x . . . . . . . . . . . (2) Now, it is given that n (A) = n (B) \Rightarrow 14 + 2 x = 4 x \Rightarrow 2 x = 14 \Rightarrow x = 7 . Hence, n (A) = 14 + 2 x = 14 + 2 (7) = 28 n (B) = 4 x = 4 (7) = 28 and n (A \cap B) = x = 7 Therefore, n (A \cup B) = n (A) + n (B) - n (A \cap B) = 28 + 28 - 7 = 49 .$

Suggest Corrections

Similar questions

A and B are two sets such that n (A - B) =14 + x, n(B - A) = 3x and n(A $\cap$ B) = x.

Draw a Venn diagram to illustrate information and if n(A) = n(B), then find the value of x.

\cap

\cup

A

B

n (A) = 20

n (A \cap B) = 4

n (A \cup B) = 42

A

B

n (A - B) = 32 + x, n (B - A) = 5 x

n (A \cap B) = x

n (A) = n (B)

x

n (A \cup B)

n (A \cup B) = 50

n (A \cap B)

Join BYJU'S Learning Program