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# Math

## Solving Problems Involving Sets

##### Example: Write the elements of the following sets: ##### To write down the elements of S, note that W represents the set of positive integers and zero. Therefore, we get: ##### Now, we write the elements of F: ##### In order to write down the elements of Q, we use the definition for d and evaluate the elements: ##### The set K, is defined in terms of the set of natural numbers N. The set of natural numbers is the set of positive integers greater than and equal to one. Thus, we have the following elements in K: ##### Example: Consider the sets given in the previous example, find the following sets: We get the following sets:   ##### . Find:  ##### a) First, we find ##### Therefore: ##### b) We get: ##### Therefore, total number of students that like both is: ##### Number of students that like neither is: ##### The Venn digram for this question is given by: ##### The Venn diagram for this problem is: 