when question ask to prove fog= I_A or I_B. what is I_A and I_B? and what is the difference between I_A and I_B

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{I} \mathrm{is} \mathrm{known} \mathrm{as} \mathrm{identity} \mathrm{function} \mathrm{which} \mathrm{is} \mathrm{y}\mathbf{=}\mathbf{x}\mathbf{.} \\ \mathrm{i}.\mathrm{e}. \mathrm{fog}=\mathrm{x} \\ \mathrm{Now} \mathrm{A} \mathrm{and} \mathrm{B} \mathrm{must} \mathrm{signify} \mathrm{the} \mathrm{domain} \mathrm{under} \mathrm{which} \mathrm{function} \mathrm{fog} \mathrm{is} \mathrm{identity} \\ \mathrm{function}. \\ \mathrm{Provide} \mathrm{complete} \mathrm{question} \mathrm{of} \mathrm{you} \mathrm{are} \mathrm{still} \mathrm{having} \mathrm{problem}. \end{gathered}$$

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