we define the relation =m (read "equal mod m") on z x z to be the set: {(p, q): m|(p-q)}. show work.
a.) give two pairs which are in the relation =4 and two pairs that are not.
b.) show the =m is an equivalence relation.

Step-by-step explanation:

a) Give two pairs which are in the relation and two pairs that are not.

As stated before, a pair is equal mod m (written ) if . Then:

b) Show the is an equivalence relation.

An equivalence relation is a binary relation that is reflexive, symmetric and  transitive.

By definition is a binary relation. Observe that:

.

In conclusion, defines an equivalence relation.

the answer is a

step-by-step explanation:

because your just changing the position of where the shape is

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere