a) Define the union, intersection, difference, and symmetric difference of two sets.________________b) What arc the union, intersection, difference, and symmetric difference of the set of positive integers and the set of odd integers?

Solution:Step-1:1. In this problem we need to define the union , intersection , difference , and symmetric difference of of two sets. UNION: The union of two sets A and B is the set containing all elements that are in A or in B ( possibly both). Then it is denoted by , we can write if and only if or . Note : Example : A= { a, b} , B = {b ,c} then . The union of sets A and B is shown by the shaded area in the venn diagram: INTERSECTION: The intersection of two sets A and B is the set containing all elements that are both in A and B. Then it is denoted by , we can write if and only if and . Note : Example : A= { a, b} , B = {b , c} then . The intersection of sets A and B is shown by the shaded area in the venn diagram: Step-2:DIFFERENCE: The difference of two sets A and B is the set containing all elements that are in A but not in B , and it is denoted by . Note : Example : A = { a, b, c} , B = { c , d} then A- B = { a , b} . A- B is shown by the shaded area in the venn diagram: SYMMETRIC DIFFERENCE: The symmetric difference of two sets A and B is the set containing all those elements which belongs either to A or to B but not to both , and it is denoted by is also expressed by . Example : A = { a, b, c} , B = { c } then . is shown by the shaded area in the venn diagram: Step-3: b) In this problem we need to find the union , intersection , difference , and symmetric difference of the set of positive integers and the set of odd integers. Let us consider , A is the set of positive integers and B is the set of odd integers.That is , A = { 1, 2 , 3, 4, 5….} and B = {......-7,-5,-3,- 1, 1, 3, 5, 7………}Therefore , .