The given assertion can be written as ‘assuming’ is given beneath

Assuming \[a\text{ }and\text{ }b\]are genuine numbers to such an extent that \[{{a}^{2}}~=\text{ }{{b}^{2}},\text{  }a\text{ }=\text{ }b\]

Let \[p:\text{ }a\text{ }and\text{ }b\]are genuine numbers to such an extent that \[{{a}^{2}}~=\text{ }{{b}^{2}}\]

\[q:\text{ }a\text{ }=\text{ }b\]

The given assertion must be refuted. To show this, two genuine numbers, \[a\text{ }and\text{ }b,\text{ }with\text{ }{{a}^{2}}~=\text{ }{{b}^{2~}}\]are required to such an extent that \[a\text{ }\ne \text{ }b\]

Allow us to consider \[a\text{ }=\text{ }1\text{ }and\text{ }b\text{ }=\text{ }\text{ }1\]

\[\begin{array}{*{35}{l}}

{{a}^{2}}~=\text{ }{{\left( 1 \right)}^{2}}  \\

=\text{ }1\text{ }and  \\

{{b}^{2}}~=\text{ }{{\left( -1 \right)}^{2}}  \\

=\text{ }1  \\

\end{array}\]

Consequently, \[{{a}^{2}}~=\text{ }{{b}^{2}}\]

In any case, \[a\text{ }\ne \text{ }b\]

Accordingly, it very well may be inferred that the given assertion is bogus.