3. In a generic Venn diagram, we must allow for all possibilities for which set(s) an element belongs to: for example, if there are two sets A, B, we must be able to represent an element r that...

Extracted text: 3. In a generic Venn diagram, we must allow for all possibilities for which set(s) an element belongs to: for example, if there are two sets A, B, we must be able to represent an element r that belongs to both sets (we might say "x is A and B"); an element y that belongs to neither set (“y is neither A nor B"); an element z that belongs to the first set only ("z is A but not B"); and an element w that belongs to the second set only ("w is B but not A"). (a) Draw a generic Venn diagram for two sets A, B, then show where the elements x, y, z, w would be placed. (b) Complete the table by drawing a generic Venn diagram with the indicated region shaded. ANB AUB AUB (c) What relationships exist between the sets An B, AnB, AUB, and AU B?