Question

Q.5) Solve the following example. [4]

A survey was conducted in class of 110 students about their favorites colourpink and

blue. Each student like at least one colour. 60 students like blue, 70 students likes pink.

How many students like both colours?
​

Answer 1

Answer:

Given that :

• n (B ∪ P) = 110 students
• n (B) = 60 students
• n (P) = 70 students
• n (B ∩ P) = ?

Now, If A ∩ B ≠ ∅, then

n (B ∪ P) = n (B) + n (P) - n (B ∩ P)

⇒ 110 = 60 + 70 - n (B ∩ P)

⇒ 110 + n (B ∩ P) = 130

⇒ n (B ∩ P) = 130 - 110

⇒ n (B ∩ P) = 20 students

Hence, 20 students like both blue and pink colour.

SOME IMPORTANT FORMULAS :

• If A ∩ B = ∅, n (A ∪ B) = n (A) + n (B)
• If A ∩ B ≠ ∅, n (A ∪ B) = n (A) + n (B) - n (A ∩ B)
• (A ∪ B)' = A' ∩ B'
• (A ∩ B)' = A' ∪ B'
• Complement laws : A ∪ A' = U & A ∩ A' = ∅
• De Morgan's Law : (A ∪ B)' = A' ∪ B' & (A ∩ B)' = A' ∪ B'
• Law of double complementation : (A')' = A
• Law of empty set and universal set : ∅' = U & U' = ∅

Answer 2

Answer:

10 people

Step-by-step explanation:

110 people in class

60 like pink and 70 like blue

so lets add 60+70

=130 likes

so let us subtract 130-110 = 20 (we did this bcause if evry one liked only one color then total no. of likeswould be only 110 likes )

so 20 likes are extra

so no. people like both colors= 20/2(because the people who like both will have likes in both colors )

so 10 people like both colours