Question

State whether the following statements are true or false. Justify yourself with the help of a short proof or a counter example. (1) There are at least two ways of describing the set {7, 8....}. (2) Any function with domain R®R is a binary operation.

Answer 1

1.True

$\{ 7,8,9,.........\}=$ set of all interger which are greater than equal to 7

$=\{ n\in \Z : n\geq 7 \}$

$=\{ n+6:n\in \Z_{>0} \}$

These are at least two way , to representing a set.

So the answer is true.

2.We know that,

If G be a set then a binary operation on G is a function that assigns each ordered pair of element of G an element of G.

Hence, any function with domain , $R$ ®$R$ is a binary operation .

Hence ,the statement is true.