10. a.If f(t) = tm and g(t) = tn, where m and n are positive integers, show that f∗g=tm+n+1∫10um(1−u)ndu.f∗g=tm+n+1∫01um(1−u)ndu. b.Use the convolution theorem to show that ∫10um(1−u)ndu=m!n!(m+n+1)!.∫01um(1−u)ndu=m!n!(m+n+1)!. c.Extend the result of part b to the case where m and n are positive numbers but not necessarily integers.

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A: For the solution follow the next step.

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Q: 4). Use rules of replacement to prove the following: a). (p^~q) (p^q) = p b). (pvq) →→ r = (p → r) ^…

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A: T(au+bv)=T(au)+T(bv)

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Q: 3) Find integers x and y such that 13x + 15y = 1.

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A: Given that

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A: Now,

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A: