Consider the binary operation table on set A ={1,2,3,6} * 1 2 3 6
13 1 2 6
21 2 3 6
32 3 1 6
61 6 6 3
i) Find 2*6 , 6*1,2*(1*6), 6*(2*3)
ii) Is * commutative ? justify
iii) Find the identity element if exists.
iv) Find the elements which has inverse
*
PLEASE ANSWER THIS FASSSTT!!
I need this now as this is my assignment question!!

(i)

2 * 6 = 6

6 * 1 = 1

2 * (1 * 6) = 2 * 6 = 6

6 * (2 * 3) = 6 * 3 = 6

(ii) * is commutative if for any a, b ∈ A, we have a * b = b * a. You can verify this visually by checking for symmetry in the table along the main diagonal (going from top left to bottom right).

* is not commutative because

6 * 1 = 1

while

1 * 6 = 6

(iii) If e is the identity, then for any a ∈ A, we have a * e = e * a = a.

Here, 2 is the identity element because 1 * 2 = 1 and 2 * 1 = 1, and the same is true if we replace 1 with 2, 3, or 6.

(iv) Let a ∈ A. a has an inverse a ⁻¹ if a * a ⁻¹ = a ⁻¹ * a = e.

We know that e = 2, so look for any pairs that map to 2. The table shows that

1 * 3 = 2   and   3 * 1 = 2

2 * 2 = 2

so 1 has an inverse of 3, 3 has an inverse of 1, and 2 has itself as its inverse (which is to be expected for the identity).

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!