Final answer:
The conditional statement is obtained by removing the 'if and only if' part. The converse is obtained by switching the hypothesis and conclusion. To determine the true value, we need to check if it holds true in all cases.
Step-by-step explanation:
The given bi-conditional statement is: 'A capital letter is vowel if and only if it is symmetrical.'
The conditional statement is obtained by removing the 'if and only if' part. So, the conditional statement is: 'If a capital letter is symmetrical, then it is a vowel.'
The converse of the bi-conditional statement is obtained by switching the hypothesis and conclusion. So, the converse is: 'If a capital letter is a vowel, then it is symmetrical.'
To determine the true value of the bi-conditional statement, we need to check if it holds true in all cases. If we find any counterexample where a capital letter is symmetrical but not a vowel, or a capital letter is a vowel but not symmetrical, then the bi-conditional statement is false. Otherwise, it is true. It is not clear if the question provides any examples to determine the true value.