3. Let H:NxNU A be the function. AEF (a) Show that function H is surjective. (b) Establish the existence of a surjection from N onto N N. Do so by explicitly devising a surjective mapping G:N + NX N. (c) Argue that the set-theoretic union U A is countable. AEF 4. Let I be an alphabet. Prove that the family P(**) of all languages over alphabet is uncountable. Following your rigorous proof to establish this proposition, write a succinct and coherent informal argument meant to persuade me of this proposition's truth. No less than 200 words and no more than 500 words are to be consumed by your written argumentation. 3. Let H:NxNU A be the function. AEF (a) Show that function H is surjective. (b) Establish the existence of a surjection from N onto N N. Do so by explicitly devising a surjective mapping G:N + NX N. (c) Argue that the set-theoretic union U A is countable. AEF 4. Let I be an alphabet. Prove that the family P(**) of all languages over alphabet is uncountable. Following your rigorous proof to establish this proposition, write a succinct and coherent informal argument meant to persuade me of this proposition's truth. No less than 200 words and no more than 500 words are to be consumed by your written argumentation