Q. 154.5( 6 Votes )

# In a survey it was found that 21 persons liked product P_{1}, 26 liked product P_{2} and 29 liked product P_{3}. If 14 persons liked products P_{1} and P_{2}; 12 persons liked product P_{3} and P_{1}; 14 persons liked products P_{2,} and P_{3} and 8 liked all the three products. Find how many liked product P_{3} only.

Answer :

Let n(P_{1}) be a number of people liking product P_{1}.

Let n(P_{2}) be a number of people liking product P_{2}.

Let n(P_{3}) be a number of people liking product P_{3}.

Then, According to the question:

n(P_{1}) = 21, n(P_{2}) = 26, n(P_{3}) = 29, n(P_{1}∩ P_{2}) = 14

n(P_{1}∩ P_{3}) = 12, n(P_{2}∩ P_{3}) = 14, n(P_{1}∩ P_{2} ∩ P_{3}) = 8.

∴ Number of people liking product P_{3} only:

= 29–(4+8+6)

= 29– 18

=11

Rate this question :

Mark the correct alternative in the following:

If A and B are two disjoint sets, then n is equal to

RD Sharma - Mathematics

If A and B are two sets such that n(A) = 20, n(B) = 25 and n= 40, then write n.

RD Sharma - MathematicsIf A and B are two sets such that n(A) = 115, n(B) = 326, n (A − B) = 47, then write .

RD Sharma - MathematicsA survey shows that 76% of the Indians like oranges, whereas 62% like bananas. What percentage of the Indians like both oranges and bananas?

RD Sharma - MathematicsIf A = {x : x ϵ N, x ≤ 7}, B = {x : x is prime, x < 8} and C = {x : x ϵ N, x is odd and x < 10}, verify that:

(i) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

(ii) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

RS Aggarwal - Mathematics

Mark the correct alternative in the following:

Let be the universal set containing 700 elements. If A, B are sub-sets of such that n (A) = 200, n (B) = 300 and n=100. Then, n=

RD Sharma - Mathematics