Give an example of set a with |a| = 5 and two disjoint partitions s1and s2ofa with |s1| = |s2|= 3.

Step-by-step explanation:

Notice the set has 5 elements (which is denoted as |A|=5). A partition of A is kind of like distributing the elements of A into as many sets as you want, without leaving any set empty (formally it's just a collection of nonempty disjoint subsets of A whose union is all of A).

In the partition we distribute the elements of A into three sets, resulting with the sets (so basically 1 and 2 are in their own sets, and 3,4,5 are all in another set). This partition is made then of 3 sets (since we distributed the elements of A into this three sets), and so

In the partition we distribute the elements of A into three sets also, resulting with the sets (so basically 4 and 5 are in their own sets, and 1,2,3 are all in another set). This partition is made then of 3 sets (since we distributed the elements of A into this three sets), and so

The partitions and are disjoint, since they don't have any element in common. The elements of the partitions are technically the SETS that are inside of them, and notice that both partitions are made of entirely different sets.

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40