Educational

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 \[ A-(A-B) \] \[ =A\cap(A-B)’ \] \[ =A\cap(A\cap B’)’ \] \[ =A\cap(A’\cup B) \]

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