Sets – Class XI – Exercise 1.6

What if my answer is a letter. That’s bad huh… 😉 I have huge respect for people that hack at numbers all day! I look at computer code instead. 😄
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Breath Math

  1. If X and Y are two sets such that n(X) = 17, n(Y) = 23 and n(X ∪ Y) = 38, find n(X ∩Y).

Solution:

It is given that: n(X) = 17, n(Y) = 23, n(X ∪ Y) = 38

n(X ∩ Y) = ?

We know that, n(X ∩Y) = n(X) + n(Y) – n(X∩Y)

38 = 17 + 23 – n(X ∩Y)

n(X ∩Y) = 40 – 38 = 2

Therefore n(X ∩Y) = 2


  1. If X and Y are two sets such that X ∪Y has 18 elements, X has 8 elements and Y has 15 elements; how many elements does X ∩Y have?

Solution:

It is given that, n(X U Y) = 18, n(X) = 8, n(Y) = 15

We know that,

n(X ∩Y) = n(X) + n(Y) – n(X∩Y)

18 = 8 + 15 – n(X∩Y)

n(X∩Y) = 23 – 18 = 5

n(X∩Y) =…

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