Final answer:
To combine a conditional statement and its converse, both must be true, establishing that each is a necessary and sufficient condition for the other. Examples include the relationship between a bachelor and being unmarried, or the relationship between squares and rectangles.
Step-by-step explanation:
A conditional statement is a logical structure that includes an 'if' clause (the antecedent) and a 'then' clause (the consequent). To combine a conditional statement and its converse, both statements must be true. This scenario typically occurs when each statement describes a necessary and sufficient condition for the other. For instance, the conditional 'If you are a bachelor, then you are unmarried' and its converse 'If you are unmarried, then you are a bachelor' can be combined because 'being a bachelor' is both necessary and sufficient to 'being unmarried', and vice versa.
Necessary means that the consequent must be true if the antecedent is true, as in the logical relationship where 'graduating with a bachelor’s degree' requires 'completing 120 credit hours'—the credit hours are necessary for the degree. Sufficient means that if the antecedent is true, it guarantees the truth of the consequent. In logical terms, we can use examples such as 'If X, then Y' to explain this relationship, where X is the sufficient condition for Y.
Marrying the two, when both conditions apply—sufficient and necessary—we find that a conditional and its converse can be true and combined. A recognizable example of such a relation is between shapes - 'If a figure is a square, then it is a rectangle,' and the converse 'If a figure is a rectangle with equal sides, then it is a square.' Both statements are true because all the sides of a square are equal (sufficient condition for it to be a rectangle), and a rectangle with equal sides must be a square (necessary condition).