4. Let n e N with n > 1, V = Z and set E = {{r,y} : x, y E Z and |x – y| = n}. Define G„ = (V, E). %3D (a) Prove that Gn is a simple graph.

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A: Given  Mt=∫s=0te-s dWs      , where W is a Brownian motion.

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A: Please refer the attached image for complete solution.

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A:

Q: 6. Find the Wronskian for the set of functions {e¬x, xe¯*, (x + 1)e¬*}.

A:

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A: This is simple question can be solve by rationalising the given function Solution is given below

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A: Answer and explanation is given below

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Q: 17) Draw the graph of a function K(m), such that S К (т) dm о

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A: Answer

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A:

Q: 18/156) If the Wronskian W of fand g is t'e' and if f(t) = t, find g(t).

A: