(a) State the definition of a compact subset of C. (b) Show that if K is a compact subset of C, and A is a closed subset of K, then also A is compact.

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Q: A: 1) min pxx + pyy s.t. xxx + αyy =ū L(x, y₁x) = px x +P₁Y + X[Xxx + xyy_ū] X: px + 1x2=0 Py + xy₁…

A: Since you have posted multiple questions, so we will solve only the first question for you. Kindly…