If a conditional statement is true, which related conditional is always true?
1. converse
2. inverse
3. contrapositive
4. bioconditional
Is it 1?
nope.
for example,
statement: if it rains, I eat pizza
converse: if I eat pizza, it rains
clearly not necessarily true
better review the topic
coverse
converse
To determine which related conditional statement is always true when the given conditional statement is true, we need to understand the definitions of converse, inverse, contrapositive, and biconditional statements.
1. Converse: The converse of a conditional statement switches the hypothesis and conclusion. For example, if the given conditional statement is "If it is raining, then the ground is wet," the converse would be "If the ground is wet, then it is raining."
2. Inverse: The inverse of a conditional statement negates both the hypothesis and the conclusion. Using the previous example, the inverse would be "If it is not raining, then the ground is not wet."
3. Contrapositive: The contrapositive of a conditional statement switches and negates both the hypothesis and the conclusion. So, using the same example, the contrapositive would be "If the ground is not wet, then it is not raining."
4. Biconditional: A biconditional statement is a single statement that combines the conditional and its converse. It implies that both the conditional and converse are true. Using the previous example, the biconditional statement would be "It is raining if and only if the ground is wet."
Now, considering the given options, if the original conditional statement is true, the related conditional statement that is always true is the contrapositive (option 3). The contrapositive shares the same truth value as the original conditional statement. So, if the conditional statement is true, its contrapositive is also true.