Week 2

 Equal sets have the exact same elements, while equivalent sets have the same number of elements. Sets D= {microrapror, anchiornis, archaeopteryx} and F= {microraptor, anchiornis, archaeopteryx} are equal, because they have the same elements. Sets T= {troodon, latenivenatrix, stenonychosaurus} and A= {allosaurus, saurophaganax, labrosaurus} are not equal, due to having different elements, but are equivalent since they have the same number of elements. 

The cardinal number of a set is the amount of unique elements within the set. Set A= {allosaurus, saurophaganax, labrosaurus} has a cardinal number of 3, while set S= {a,l,l,o,s,a,u,r,u,s} has a cardinal number of 8 (note how, because “a” occurs twice and “u” occurs twice, the second occurrences of both elements do not count towards the cardinal number as they are not unique.)

Vent diagrams provide a useful visual method to understand the relationships between sets. Venn diagrams can, however, be confusing at times, and Venn diagrams for a greater number of sets than three no longer accurately represent all relationships between all sets. 

In the context of set theory- “And” statements imply only the elements that occur in two sets simultaneously, the intersection of two sets, while “or” statements imply any element that occurs in either set, the union of two sets.