Assume for the sets S, T, which are in the universal set , that we know S T a) Draw as many different diagrams as you can portraying the possible relationships between S and T. b) Identify 2 other set relationships that must also be true among the sets S,T, SC, T. Suppose another student drew their diagram as shown to the right. Are your answers to part b still true in this diagram? How could you shade the diagram to show how your set relationships are true in this diagram? Assume for the sets H, K, which are in the universal set , that we know H & K. a) Draw at least three different diagrams that portray the possible relationships between H and K. b) Use the diagrams to explain why H element of K." c) Use the diagrams to explain why H elements of K and some elements of H are elements of K." Sc T K is not equivalent to the claim "each element of H is not an K is not equivalent to the claim "some elements of H are not d) Use the diagrams to explain why H K is equivalent to the claim "there exists an element of H that is not an element of K."