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Let * be binary operation on Q defined by $ a*b=\large\frac{3ab}{5} $ show that * is commutative as well as associative. Also find its identity element if it exists.
cbse
class12
modelpaper
2012
sec-b
q12
math
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asked
Feb 4, 2013
by
thanvigandhi_1
edited
Jul 26, 2013
by
sreemathi.v
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Related questions
Let * be binary operation of N x N defined by (a,b)*(c,d)=(a+c,b+d). Show that * is commutative as well as associative. Find the identity element for the operation * on N x N, if any.
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Let * be binary operation of N x N defined by (a,b)*(c,d)=(a+c, b+d). Show that * is commutative as well as associative. Find the identity element for the operation * on N x N, if any.
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Let A = N x N and * be a binary operation on A defined by (a,b)*(c,d)=(ac,bd), show that : (i) (A*) is commutative. (ii) (A*) is associative (iii) Find the identity element, if any, in A.
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Let\(A=N \times N \,and\, \ast \) be the binary operation on \(A\) defined by \( (a, b) \ast (c, d) = (a + c, b + d)\). Show that \(\ast\) is commutative and associative. Find the identity element for \(\ast\) on \( A \), if any.
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Let * be a binary operation on set Q of rational numbers defined as a*b = \( \large\frac{3ab}{7} \). Write the identity for * , if any.
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(i) Is the binary operation defined on set N, given by \( a*b = \large\frac{a+b}{2}\) for all a,b \( \in\) N. commutative? (ii) Is the above binary operation associative?
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Let * be the binary operation on N given by p * q = LCM of p and q. Find (i) 12 * 56 (ii) whether * is commutative? (iii) whether * is associative (iv) identity of * in N.
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