Question

State the converse, inverse and contrapositive of the conditional statement: 'If a sequence is bounded, then it is convergent.

Answer 1

Hint: Use the concept, that if there is a conditional statement which is as follows:
If X then Y, then we will have the following statements for the converse, inverse and contrapositive.
Converse: If Y, then X
Inverse: If not X, then not Y
Contrapositive: If not Y then not X.

Complete step-by-step answer:
In the question, we have to state the converse, inverse and contrapositive of the conditional statement: 'If a sequence is bounded, then it is convergent.
If X then Y, then we will have the following statements for the converse, inverse and contrapositive.
So, take the statement X \[\equiv \] a sequence is bounded
and statement Y\[\equiv \] it is convergent
Now, we have following statements:
Converse: If Y, then X or “If a sequence is convergent then it is bounded.”
Inverse: If not X, then not Y or “If a sequence is not bounded then it is not convergent.”
Contrapositive: If not Y then not X or “If a sequence is not convergent then it is not bounded.”
So, above three statements are required statements for converse, inverse and contrapositive of the conditional statement: 'If a sequence is bounded, then it is convergent.

Note: It is important to note that we should have been given with the conditional statement only and just any statement. Then only we will be able to find the converse, inverse and contrapositive of the conditional statement.