Question

let A={a1,a2,a3,a4} where a1>a2>a3>a4. The total number of unordered pairs of disjoint subsets is equal to what?​

Answer 1

the total no of unordered pairs of disjoint subsets is equal to 41

Answer 2

Step-by-step explanation:

Given let A={a1,a2,a3,a4} where a1>a2>a3>a4. The total number of unordered pairs of disjoint subsets is equal to what?

• Now the elements of A = {a1, a2, a3, a4}
• Now we need to find total number of unordered pairs of disjoint subsets.  
• Assume P = {    } and Q = {  }
• Now disjoint means A Ո B = {φ} as there is no common element.
• So we need to know the number of pairs that can be done from (P,Q)
• Now A = {a1,a2,a3,a4}
• Now we will make two subsets that is disjoint P = {  } and Q = {  }
• The element a1 should be either in P or Q. It cannot be in two sides since it will be common and third option is there is no element in either of the two.
• Now there are 4 elements and there are 3 options in all the 4 elements.
• So from these 4 elements we can distribute 3 elements.
• The subset in PQ so that there is no common will be 3^4
• So the combination will be from two subsets like P = {φ } and Q = {φ} and these two are null set and P Ո Q = φ
• Now P and Q count will be once.in 3^4
• Also Q = {φ} and P = {φ}
• These cases are similar and will be counted once.
• The other pairs would have been counted twice.
• So total number of subsets will be 3^4 + 1 / 2
•                                                      82 / 2
•                                                        = 41
• Therefore total number of unordered pairs will be 41

Reference link will be

https://brainly.in/question/1358316