Question

Out of 500 car owners investigated, 400 owned car a and 200 owned car b, 50 owned both a and b cars. Is this data correct?

Answer 1

Step-by-step explanation:

The above pic is the answer

Answer 2

Answer:

Number of cars = n(U) = 500

Number of people who owned car A = n(A) = 400

Number of people who owned car B = n(B) = 200

Number of people who owned both A and B = n(A∩B) = 50

n(U) = n(A) + n(B) - n(A∩B)

⇒ n(AUB) = n(A) + n(B) - n(A∩B)

⇒ 500 = 400 + 200 - 50

⇒ 500 = 600 - 50

⇒ 500 = 550

Hence, the data is incorrect.

MORE INFORMATION -

• (A∩B) ≠ ∅, n(AUB) = n(A) + n(B) - n(A∩B)
• (A∩B) = ∅, n(AUB) = n(A) + n(B)
• (A∩B)' = A' U B'
• (AUB)' = A'∩B'
• Complement of a subset A of universal set U is the set of all elements of U which are not the elements of A.
• Intersection is the set of elements which are common.
• Union is the set of elements which are either in A or in B.