An operation * is defined on the set `Z` of non-zero integers by a*b=`a/b` for all `a ,\ b in Z` . Then the property satisfied is (a) closure (b) commutative (c) associative (d) none of these

The binary operation defined on the set z of all integers as a ** b = |a-b| - 1 is

The binary operation * defined on N by a*b= a+b+a b for all a ,\ b in N is (a) commutative only (b) associative only (c) commutative and associative both (d) none of these

If a binary operation * is defined on the set Z of integers as a * b=3a-b , then the value of (2 * 3) * 4 is

On Z an operation * is defined by a*b= a^2+b^2 for all a ,\ b in Z . The operation * on Z is (a)commutative and associative (b)associative but not commutative (c) not associative (d) not a binary operation

Check the commutativity of * on Z defined by a*b=a+b+a b for all a ,\ b in Z .

Let * be a binary operation on the set Q_0 of all non-zero rational numbers defined by a*b= (a b)/2 , for all a ,\ b in Q_0 . Show that (i) * is both commutative and associative (ii) Find the identity element in Q_0 (iii) Find the invertible elements of Q_0 .

If the operation * is defined on the set Q - {0} of all rational numbers by the rule a * b=(a b)/4 for all a ,\ b in Q - {0} . Show that * is commutative on Qdot - {0}

A binary operation * on Z defined by a*b= 3a+b for all a ,\ b in Z , is (a) commutative (b) associative (c) not commutative (d) commutative and associative

Let '**' be the binary operation defined on the set Z of all integers as a ** b = a + b + 1 for all a, b in Z . The identity element w.r.t. this operations is

Let * be a binary operation on Q_0 (set of non-zero rational numbers) defined by a*b= (3a b)/5 for all a ,\ b in Q_0 . Show that * is commutative as well as associative. Also, find the identity element, if it exists.