If X and Y are two non-empty sets such that n(X) = 17, n(Y) = 23 and n(X ∪ Y) = 38, then n( X ∩ Y ) is
2
Concept:
Countable set - A countable set is defined as the number of elements present in a given set. It is represented by n(A) .
The fundamental formula for countable sets is
n(A U B) = n(A) + n(B) - n( A ∩ B )
Calculation:
Set X has 17 elements .
Set Y has 23 elements .
Set X U Y has 38 elements .
Substituting the values,
38 = 17 + 23 - n(X ∩ Y)
38 = 40 - n(X ∩ Y)
n(X ∩ Y) = 40 - 38
n(X ∩ Y) = 2
Thus, there are 2 elements common to both X and Y.
Important Questions from Operations on Sets
What is the number of natural numbers less than or equal to 1000 which are neither divisible by 10 nor 15 nor 25?
If A = {x ∈ R : x 2+ 6x - 7 < 0} and B = {x ∈ R : x 2+ 9x + 14 > 0}, then which of the following is/are correct?
1. (A ∩ B) = (-2, 1)
2. (A - B) = (-7, -2)
Select the correct answer using the code given below:A, B, C and D are four sets such that A ∩ B = C ∩ D = ϕ. Consider the following:
1. A ∪ C and B ∪ D are always disjoint.
2. A ∩ C and B ∩ D are always disjoint.
Which of the above statements is/are correct?A coin is tossed three times. Consider the following events:
A: No head appears
B: Exactly one head appears
C. At least two heads appear
Which one of the following is correct?
If C = { 2, 4, 6, 8, 10, 12, 14, 16 }, and D = {5, 10, 15, 20}, then the number of elements in the set D - C is:
