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Byju's Answer
Standard IX
Mathematics
Associative Property
If A = -2...
Question
If
A
=
{
−
2
,
3
,
0
},
B
=
{
−
1
,
−
4
} and
C
=
{
1
,
−
2
}. then prove
(
A
∪
B
)
∪
C
=
A
∪
(
B
∪
C
)
Open in App
Solution
Given,
A
=
{
−
2
,
3
,
0
},
B
=
{
−
1
,
−
4
} and
C
=
{
1
,
−
2
}
First take L.H.S
(
A
∪
B
)
∪
C
(
A
∪
B
)
=
{
−
1
,
−
2
,
−
4
,
0
,
3
}
(
A
∪
B
)
∪
C
=
{
−
1
,
−
2
,
−
4
,
0
,
1
,
3
}
Similarly, take R.H.S
A
∪
(
B
∪
C
)
B
∪
C
=
{
−
1
,
−
2
,
−
4
,
1
}
A
∪
(
B
∪
C
)
=
{
−
1
,
−
2
,
−
4
,
0
,
1
,
3
}
So, L.H.S
=
R.H.S
Hence, proved.
Suggest Corrections
0
Similar questions
Q.
If
A
=
{
1
,
2
,
3
},
B
=
{
2
,
4
} and
C
=
{
1
,
2
}, then prove
(
A
∪
B
)
∪
C
=
A
∪
(
B
∪
C
)
Q.
If
A
=
{
6
,
1
,
4
,
7
},
B
=
{
4
,
2
} and
C
=
{
8
,
4
,
2
}, then prove
(
A
∪
B
)
∪
C
=
A
∪
(
B
∪
C
)
Q.
If
A
∪
B
=
A
∪
C
and
A
∩
B
=
A
∩
C
, then prove that
B
=
C
.
Q.
If
X
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
}
is the universal set and
A
=
{
1
,
2
,
3
,
4
}
,
B
=
{
2
,
4
,
6
,
8
}
,
C
=
{
3
,
4
,
5
,
6
}
verify the following.
(a)
A
∪
(
B
∪
C
)
=
(
A
∪
B
)
∪
C
(b)
A
∩
(
B
∪
C
)
=
(
A
∩
B
)
∪
(
A
∩
C
)
(c)
(
A
′
)
′
=
A
Q.
If
A
=
{
−
3
,
−
1
,
0
,
4
,
6
,
8
,
10
}
,
B
=
{
−
1
,
−
2
,
3
,
4
,
5
,
6
}
,
a
n
d
C
=
{
−
6
,
−
4
,
−
2
,
2
,
4
,
6
}
show that
A
∪
(
B
∩
C
)
=
(
A
∪
B
)
∩
(
A
∪
C
)
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