Let * be a binary operation on `R` defined by a*b= `a b+1` . Then, * is (a)commutative but not associative (b)associative but not commutative (c)neither commutative nor associative (d) both commutative and associative

Let * be a binary operation on R defined by a*b=a b+1 . Then, * is commutative but not associative associative but not commutative neither commutative nor associative (d) both commutative and associative

Subtraction of integers is (a)commutative but not associative (b)commutative and associative (c)associative but not commutative (d) neither commutative nor associative

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

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 a binary operation on Z defined by a*b= a+b-4 for all a ,\ b in Zdot Show that * is both commutative and associative.

Examine whether the binary operation ** defined on R by a**b=a b+1 is commutative or not.

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

Show that the binary operation * on Z defined by a*b= 3a+7b is not commutative.

Let * be a binary operation on Q-{0} defined by a*b=(a b)/2 for all a ,\ b in Q-{0} . Prove that * is commutative on Q-{0} .

If * is a binary operation in N defined as a*b =a^(3)+b^(3) , then which of the following is true : (i) * is associative as well as commutative. (ii) * is commutative but not associative (iii) * is associative but not commutative (iv) * is neither associative not commutative.