Question

1. How do you construct an inductive proof?
2. What does it mean for a set to be closed under an operation?
3. What is set union?
4. What is set intersection?
5. What is another name for the intersection of all inductive sets?

Answer 1

Inductive proof has 2 cases.first one is the base case.we have to prove the statement for n=0

Second case is the induction step,it proves statement is true for any value n=k then it also hold true for n=k+1

Thus induction proof is done

for a set to be closed under an operation if the performance of the operation on given set always produces a member in the set

If any operation is performed on 2 elements in the set then the resultant value should be in the same set then it is called a set closed under operation

Set union is collection of all the elementsin set if this Operation is performed on 2sets then total elements in sets shoud be in the union set

If intersection operation is performed on 2 sets then the resultant set is common elements form both the sets

To find out the common elements between 2sets intersection operation is used