Sets
Sponsor Area
A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A ∪ B) is
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3/5
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0
-
1
-
2/5
C.
1
A = {4, 5, 6} , B = {1, 2, 3, 4} .
Obviously P (A ∪ B) = 1.
Sponsor Area
If A, B and C are three sets such that A ∩ B = A∩ C and A ∪ B = A ∪ C, then
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A = B
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A = C
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B = C
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A ∩ B = φ
C.
B = C
A ∪ B = A ∪ C
⇒ n (A ∪ B) = n(A ∪ C)
⇒ n(A) + n(B) – n(A ∩ B)
= n(A) + n(C) – n(A ∩C)
n(B) = n(C)
If X = {4n - 3n-1 : n ε N} and Y = {9(n-1):n εN}; where N is the set of natural numbers,then X U Y is equal to
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N
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Y-X
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X
-
Y
D.
Y
We have X = {4n - 3n-1 : n ε N}
X = {0,9,54,243,.....} [put n = 1,2,3....]
Y = {9(n-1):n ε N}
Y = {0,9,18,27,......}[Put n = 1,2,3....]
It is clear that
X ⊂ Y
Therefore, X U Y = Y
Let A and B be two events such that 
where 
stands for complement of event A. Then events A and B are
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equally likely and mutually exclusive
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equally likely but not independent
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independent but not equally likely
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mutually exclusive and independent
C.
independent but not equally likely
Also P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
⇒ P(B) = 5/6 – 3/4 + 1/4 = 1/3
P(A) P(B) = 3/4 – 1/3 = 1/4 = P(A ∩ B)
Hence A and B are independent but not equally likely.
Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is
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256
-
220
-
219
-
211
C.
219
Given, n(A) =2, n(B) = B
The number of subsets of AXB having 3 or more elements,
=
Sponsor Area
Mock Test Series
Mock Test Series