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Standard XII
Mathematics
Commutative Law of Binary Operation
The number of...
Question
The number of commutative binary operations that can be defined on a set of 2 elements is
(a) 8
(b) 6
(c) 4
(d) 2
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Solution
(d) 2
The number of commutative binary operations on a set of n elements is
n
n
n
-
1
2
.
Therefore,
Number of commutative binary operations on a set of 2 elements =
2
2
2
-
1
2
=
2
1
=
2
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Similar questions
Q.
The number of binary operation that can be defined on a set of 2 elements is
(a) 8
(b) 4
(c) 16
(d) 64
Q.
Is the binary operation
∗
defined on the set of
integer
z
by the rule
a
∗
b
=
a
−
b
+
2
commutative ?
Q.
Which of the following is true?
(a) * defined by
a
*
b
=
a
+
b
2
is a binary operation on Z
(b) * defined by
a
*
b
=
a
+
b
2
is a binary operation on Q
(c) all binary commutative operations are associative
(d) subtraction is a binary operation on N
Q.
Consider a set x
=
{
a, b, c, d
}
. The number of binary operations that can be defined on x is?
Q.
Let
x
be non-empty set.
P
(
x
)
be its power set. Let * be an operation defined on element of
P
(
x
)
b
y
,
A
∗
B
=
A
∩
B
∀
A
,
B
∈
P
(
x
)
.
Then
(i) Prove that * is a binary operation in
P
(
x
)
(ii) is * associative?
(iii) Is * commutative?
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