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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?
cbse
class12
modelpaper
2008-1
sec-b
q11
math
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asked
Dec 20, 2012
by
thanvigandhi_1
edited
Jul 15, 2013
by
sreemathi.v
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(i) Is the binary operation * defined on set N, given a * b = \( \large\frac{a+b}{2} \) for all a, b \( \in\) N, comutative? (ii) Is the above binary operation * associative ?
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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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For each binary operation * defined below, determine whether * is (i) commutative (ii) associative \( a*b = \large\frac{ab}{2}\) on Q?
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'*' is a binary operation defined on Q. Find which of the following binary oprations are associative and which are commutative : $(i) a*b=a-b\: for \: a,b \in Q (ii) a*b = \large\frac{ab}{4}$$\: for \: a,b \in Q.$
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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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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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