โ To verify that two sets A and B are equal, written A = B, show that for every x, if x โ A, then x โ B, and if x โ B, then x โ A.
โ To verify that two sets A and B are not equal, written A =ฬธ B, find at least one element that is in A but not in B, or find at least one element that is in B but not in A. One or the other conditions sufces; you need not (and may not be able to) show both conditions.
โ To verify that A is a subset of B, written A โ B, show that for every x, if x โ A,