Question

is there a whole number P first that p÷p=p? is there any whole no. for which this relation does not hold good

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

QUESTION : 1

Is there a whole number P first that

$\displaystyle \: \frac{p}{p} = p$

QUESTION : 2

Is there any whole no. for which the relation

$\displaystyle \: \frac{p}{p} = p$

does not hold good

EVALUATION

The set of whole numbers is

$W = \{ 0,1,2,3,4,5,6,7,8,9,....... \}$

ANSWER TO QUESTION : 1

Since

$\displaystyle \: \frac{p}{p}$

is defined

So

$p \ne \: 0$

Now

$\displaystyle \: \frac{p}{p} = p \: \: \: \: gives$

${p}^{2} = p$

$\implies \: {p}^{2} - p = 0$

$\implies \: p(p - 1) = 0$

$\implies \: p = 0 \: , \: 1$

$since \: \: p \ne \: 0$

So p = 1

So p = 1 is the only whole number for which the relation

$\displaystyle \: \frac{p}{p} = p \: \: \: holds$

ANSWER TO QUESTION : 2

From above we see that p = 1 is the only whole number for which the relation

$\displaystyle \: \frac{p}{p} = p \: \: \: holds$

So for any other whole number other than 1 the relation

$\displaystyle \: \frac{p}{p} = p \: \: \: does \: not \: hold$