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Intersection of Set, Properties of Intersection is considered one of the most asked concept.
27 Questions around this concept.
If and
Find
In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two
languages. If the number of persons, who speak only English is and the number of persons who speak only
Hindi is , then the eccentricity of the ellipse
is:
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An organization awarded 48 medals in event ‘A’, 25 in event ‘B’ and 18 in event ‘C’. If these medals went to
total 60 men and only five men got medals in all the three events, then, how many received medals in exactly
two of three events ?
The intersection of sets A and B is the set of all elements which are common to both A and B. The symbol ‘∩ ‘is used to denote the intersection.
Symbolically, we write A ∩ B = {x: x ∈ A and x ∈ B}
For example, let A = { 2, 4, 6, 8 } and B = { 2, 3, 5, 8 }, then A ∩ B = { 2, 8 }
If A and B are two sets such that A ∩ B = φ, then A and B are called disjoint sets.
For example, let A = { 2, 4, 6, 8 } and B = { 1, 3, 5, 7 }. Then A and B are disjoint sets because there are no elements which are common to A and B.
Properties of intersection
A B = B
A (Commutative law).
( A B )
C = A
( B
C ) (Associative law).
A
=
,
A U = A (Law of
and U).
A A = A (Idempotent law)
If A is subset of B, then A B = A
Distributive laws
1. A ( B
C ) = ( A
B )
( A
C ) i. e.,
distributes over
This can be seen easily from the following Venn diagrams
LHS:
RHS:
2. A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
This can be seen easily from the following Venn diagrams
LHS:
RHS:
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