(a) True or False? In R2, any binary classification datasets with 3 data points can be perfectly separated by a Hard-margin SVM using a Euclidean plane (aka without any non-linear kernels). If you think it is correct, please briefly describe your reason. If you think it is incorrect, please provide some counter-examples. (5 points) (b) True or False? In R2, any binary classification datasets with 4 data points can be perfectly separated by a Hard-margin SVM using a Euclidean plane (aka without any non-linear kernels). If you think it is correct, please briefly describe your reason. If you think it is incorrect, please provide some counter-examples. (5 points) (c) Suppose k is a kernel with feature map , that is, for feature vectors x,z,k(x,z)=(x)T(z). Now we construct a new kernel k(x,z)=ck(x,z), where cR+. Please write a corresponding feature map for kernel k, in terms of c and . You need to elaborate your answer in details. There could be multiple correct solutions and you will only need one feasible here. (5 points) (d) Suppose k1 and k2 are two kernels with feature map 1 and 2, that is, for feature vectors x,z,k1(x,z)= 1(x)T2(z) and k2(x,z)=2(x)T2(z). Now we construct a new kernel k(x,z)=k1(x,z)k2(x,z). Please write a corresponding feature map for kernel k, in terms of 1 and 2. You need to elaborate your answer in details. There could be multiple correct solutions and you will only need one feasible here. (5 points)