Find How Many Speak Hindi and English Find How Many Speak Hindi and English Question: In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find: (i) how many can speak both Hindi and English (ii) how many can speak Hindi only (iii) how many can speak English only Solution

Find Percentage of Indians Who Like Both Orange and Bananas Find Percentage of Indians Who Like Both Orange and Bananas Question: A survey shows that 76% of the Indians like orange, whereas 62% like bananas. What percentage of the Indians like both orange and bananas? Solution \[ n(O\cup B)=n(O)+n(B)-n(O\cap B) \] Since every Indian likes

Find n(B), n(A−B) and n(B−A) Find n(B), n(A−B) and n(B−A) Question: Let \( A \) and \( B \) be two sets such that: \[ n(A)=20,\quad n(A\cup B)=42,\quad n(A\cap B)=4 \] Find: \[ (i)\ n(B) \] \[ (ii)\ n(A-B) \] \[ (iii)\ n(B-A) \] Solution (i) Find \( n(B) \) \[ n(A\cup B)=n(A)+n(B)-n(A\cap B) \]

Find How Many Like Both Coffee and Tea Find How Many Like Both Coffee and Tea Question: In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many like both coffee and tea? Solution \[ n(C\cup T)=n(C)+n(T)-n(C\cap T) \] \[ 70=37+52-n(C\cap

Find How Many Teachers Teach Physics Find How Many Teachers Teach Physics Question: In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach physics and mathematics. How many teach physics? Solution \[ n(M\cup P)=n(M)+n(P)-n(M\cap P) \] \[ 20=12+n(P)-4 \] \[ 20=8+n(P) \] \[ n(P)=20-8 \]

Find Number of Elements in Q Find Number of Elements in Q Question: If \( P \) and \( Q \) are two sets such that \[ n(P)=40,\quad n(P\cup Q)=60,\quad n(P\cap Q)=10 \] how many elements does \( Q \) have? Solution \[ n(P\cup Q)=n(P)+n(Q)-n(P\cap Q) \] \[ 60=40+n(Q)-10 \] \[ 60=30+n(Q) \] \[ n(Q)=60-30

Prove That (A − B) ∪ (A ∩ B) = A Prove That (A − B) ∪ (A ∩ B) = A Question: For any two sets \( A \) and \( B \), prove that: \[ (A-B)\cup(A\cap B)=A \] Solution \[ (A-B)\cup(A\cap B) \] \[ =(A\cap B’)\cup(A\cap B) \] \[ =A\cap(B’\cup B) \] \[

Find n(A∩B) If n(A∪B)=50, n(A)=28 and n(B)=32 Find n(A∩B) Question: If \( A \) and \( B \) are two sets such that \[ n(A\cup B)=50,\quad n(A)=28,\quad n(B)=32 \] find \( n(A\cap B) \). Solution \[ n(A\cup B)=n(A)+n(B)-n(A\cap B) \] \[ 50=28+32-n(A\cap B) \] \[ 50=60-n(A\cap B) \] \[ n(A\cap B)=60-50 \] \[ n(A\cap B)=10

Prove That A ∪ (B − A) = A ∪ B Prove That A ∪ (B − A) = A ∪ B Question: For any two sets \( A \) and \( B \), prove that: \[ A\cup(B-A)=A\cup B \] Solution \[ A\cup(B-A) \] \[ =A\cup(B\cap A’) \] \[ =(A\cup B)\cap(A\cup A’) \] \[ =(A\cup

Prove That A − (A − B) = A ∩ B Prove That A − (A − B) = A ∩ B Question: For any two sets \( A \) and \( B \), prove that: \[ A-(A-B)=A\cap B \] Solution \[ A-(A-B) \] \[ =A\cap(A-B)’ \] \[ =A\cap(A\cap B’)’ \] \[ =A\cap(A’\cup B) \]