Let * `R*Rvec` given by `(a , b) vec (a+4b^2`) is a binary operation. Compute `(-5)*2*0)dot`

Show that quad *:R xx R rarr R given by (a,b)rarr a+4b^(2) is a binary operation.

Is * defined by a^(*)b=(a+b)/(2) is binary operation on Z.

Let * RxxRrarrR be a binary operation given by a*b=a+4b^(2) Then compute (-5)*(2*0)

Determine whether or not the definition of * On R ,define * by a*b=a+4b^(2) gives a binary operation.In the event that * is not a binary operation give justification of this. Here,Z^(+) denotes the set of all non-negative integers.

Let S={a,b,c}. Find the total number of binary operations on S.

Which of the following is true? * 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

Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this. (i) On Z^+ , define ∗ by a ∗ b = a – b (ii) On Z^+ , define ∗ by a ∗ b = ab (iii) On R , define ∗ by a ∗ b = ab^2 (iv) On Z^+ , define ∗ by a ∗ b = |a – b| (v) On Z^+ , define ∗ by a ∗ b = a

Let * be a binary operation defined by a*b=3a+4b-2. Find 4^(*)5

Show that the quad vv:R rarr R given by and the and the given by quad (a,b)rarr min{a,b) are binary operations.