Let fC1 be a strictly concave function over D. If there exists some xD so that f(x)=0 then xmaximizes the function f over D.2. If X is a compact set and YX and Y, then Y is a compact set.3. If x is the solution to the maximization of fC1 over the domain D then the slope of f at xmust be zero. 4. Let f and g be twice continuously dierentiable functions. if f is concave and if g is strictly increasing, then the function g(f(x))is concave.5. If xis the maximum for the functions f+g over the domain D, then xis the maximum for both the functions f and g over D. 6. If AB and B is convex, then A is convex. 7. Let P,R, and Q be propositions. The proposition form((PR)Q)is equivalent to the propositional formQ(PR).