Question

A={x:x€N} and B = {log (base10) 1, log (base7 )7, log (base3) 9}, then find B - A.​

Answer 1

Doesn't the statement $A=\{x:x\in\mathbb {N}\}$ mean that A is the set of all natural numbers?

Well, it is. Thus we can say that $A=\mathbb {N}.$

Then what about B?

$\log_{10}1=0\\\\\log_77=1\\\\\log_39=2$

Hence,

$B=\{0,\ 1,\ 2\}$

Or,

$B=\{x:x\in\mathbb{Z},\ 0\leq x\leq 2\}$

What B - A means is that it is a set whose elements are in B but not in A.

$B-A=\{x:x\in B,\ x\notin A\}$

Since $B=\{0,\ 1,\ 2\},$ the elements in B - A can be 0, but not 1 and 2 because they're also in A. Hence,

$\Large\boxed {B-A=\{0\}}$

#answerwithquality

#BAL