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Byju's Answer
Standard XII
Mathematics
Binary Operation
If a * b deno...
Question
If
a
∗
b
denotes the larger of
′
a
′
and
′
b
′
and if
a
o
b
=
(
a
∗
b
)
+
3
, then write the value of
(
5
)
o
(
10
)
, where
∗
and
o
are binary operations.
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Solution
Given that
a
o
b
=
(
a
∗
b
)
+
3
∴
(
5
)
o
(
10
)
=
(
5
∗
10
)
+
3
=
10
+
3
[
∵
a
∗
b
= larger of
a
and
b
]
=
13
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Similar questions
Q.
If a * b denotes the larger of 'a' and 'b' and if aob = (a * b) + 3, then write the value of (5) o (10), where * and o are binary operations.
Q.
If
a
∗
b
denotes the larger of
′
a
′
and
′
b
′
and if
a
o
b
=
(
a
∗
b
)
+
3
, then write the value of
(
5
)
o
(
10
)
, where
∗
and
o
are binary operations.
Q.
If
a
∗
b
denotes the larger of
′
a
′
and
′
b
′
and if
a
o
b
=
(
a
∗
b
)
+
3
,
then write the value of
(
5
o
10
)
,
where
∗
and
o
are binary operations.
Q.
Let
A
and
B
be two square matrices of order
3
and
A
B
=
O
3
, where
O
3
denotes the null matrix of order
3
. Then,
Q.
Consider the binary operations
∗
:
R
×
R
→
R
and
o
:
R
×
R
→
R
defined as
a
∗
b
=
|
a
−
b
|
and
a
o
b
=
a
,
∀
a
,
b
∈
R
. Show that
∗
is commutative but not associative, o is associative but not commutative. Further, show that
∀
a
,
b
,
c
∈
R
,
a
∗
(
b
o
c
)
=
(
a
∗
b
)
o
(
a
∗
c
)
. [If it is so, we say that the operation
∗
distributes over the operation o]. Dose o distribute over
∗
? Justify your answer
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