Sets

3. Equality of Sets

Set A is equal to set B if they both have the same members, i.e if every element which belongs to A also belongs to B and if every element which belongs to B also belongs to A. We denote the equality of sets A and B by:

A = B

Example 5.1 Let A = {1, 2, 3, 4} and B = {3, 1, 4, 2}. Then A = B,

that is {1,2,3,4} = {3,1,4,2}, since each of the elements 1,2,3 and 4 of A belongs to B and each of the elements 3,1,4 and 2 of B belongs to A. Note therefore that a set does not change if its elements are rearranged.

Example 5.3 Let E={x | x²–3x = -2}, F={2,1} and G ={1,2,2, 1},

Then E= F= G