Question

4. Start with the following statement:

Vertical angles are congruent.
a. State the conditional and three other forms of the statement.
b. If you know that a statement is true, what do you know about the truth of its converse, inverse, and contrapositive? Use at least one truth table and at least one property to support your reasoning.

Answer 1

A)
If angles are vertical, then they are congruent; conversely if angles are congruent then they are vertical. So in such case following statements can be deduced:
Conditional: True
Converse:False
Inverse:False
Contrapositive:True

B) If a statement is true, the inverse is also logically true. Likewise, when the converse is true, the contrapositive is also logically true . So in such a case:
statement: if p then q
converse: if q then p
inverse: if not p then not q
contrapositive: if not q then not p