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Byju's Answer
Standard XII
Mathematics
Definition of Sets
Verify the fo...
Question
Verify the following identities where A = {1, 2, 3, 4, 5}, B = {2, 3, 5, 6}, C = {4, 5, 6, 7}
A
∩
(
B
∪
C
)
=
(
A
∩
B
)
∪
(
A
∩
C
)
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Solution
A{
1
,
2
,
3
,
4
,
5
}
B{
2
,
3
,
5
,
6
}
C{
4
,
5
,
6
,
7
}
(
B
∪
C
)
=
2
,
3
,
4
,
5
,
6
,
7
A
∩
(
B
∪
C
)
=
2
,
3
,
4
,
5
...(1)
(
A
∩
B
)
=
2
,
3
,
5
(
A
∩
C
)
=
4
,
5
(
A
∩
B
)
∪
(
A
∩
C
)
=
2
,
3
,
4
,
5
...(2)
From (1) and (2)
A
∩
(
B
∪
C
)
=
(
A
∩
B
)
∪
(
A
∩
C
)
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0
Similar questions
Q.
Verify the following identities where A = {1, 2, 3, 4, 5}, B = {2, 3, 5, 6}, C = {4, 5, 6, 7}
A
∪
(
B
∩
C
)
=
(
A
∪
B
)
∩
(
A
∪
C
)
Q.
Given A
=
{
1
,
2
,
3
,
4
}
, B
=
{
3
,
4
,
5
,
6
}
and C
=
{
6
,
7
}
. Verify that (A
∩
B)
∩
C = A
∩
(B
∩
C).
Q.
Verify n (A
∪
B
∪
C) = n (A) + n(B) + n (C) – n(A
∩
B) – (B
∩
C) – n(A
∩
C) + (A
∩
B
∪
C) for the following sets A = {1, 3, 5, 6, 8}, B = {3, 4, 5, 6} and C = {1, 2, 3, 6}
Q.
Verify the validity of the identity
(
a
+
b
+
c
)
2
=
a
2
+
b
2
+
c
2
+
2
a
b
+
2
b
c
+
2
c
a
for the following given values.
1.
a
=
2
b
=
4
c
=
6
2.
a
=
5
b
=
−
2
c
=
3
3.
a
=
−
2
b
=
3
c
=
−
4
Q.
Let A = {0, 1, 2, 3, 4}, B= {1, -2, 3, 4, 5, 6} and C = {2, 4, 6, 7}.
(i) Show that
A
∪
(
B
∩
C
)
=
(
A
∪
B
)
∩
(
A
∪
C
)
.
(ii) Verify this relation using Venn diagram.
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