The inverse of conditional A is given below. Write conditional A, its converse,and its contrapositive. Explain your reasoning.
If I received a detention,then I did not arrive at school on time.
If
p=I receive a detention
q=I did not arrive at school on time
the given proposition is therefore:
p->q
contrapositive = ¬q -> ¬p
inverse = ¬p -> ¬q
converse = q -> p
Notes:
1. the inverse of the inverse of A is A itself.
2.the proposition and its contrapositive are logically equivalent.
3.the inverse and the converse are logically equivalent. BUT the proposition and the converse are NOT logically equivalent.
Des
Can you explain if you still have problems?
This response answers the question you had in the other post under the name of Cassie.
To determine the conditional statement, its converse, and its contrapositive, we need to understand the structure of the original statement: "If I received a detention, then I did not arrive at school on time."
The original statement can be written as:
Conditional A: If P, then Q
P: I received a detention
Q: I did not arrive at school on time
Now, let's determine the inverse, converse, and contrapositive:
1. Inverse:
The inverse statement simply negates both the antecedent (P) and the consequent (Q) of the conditional statement. In other words, if P is true, it becomes false, and if Q is true, it becomes false.
Negating P: I did not receive a detention
Negating Q: I arrived at school on time
Inverse A: If I did not receive a detention, then I arrived at school on time.
2. Converse:
The converse of a conditional statement switches the positions of the antecedent (P) and the consequent (Q).
Converse A: If I did not arrive at school on time, then I received a detention.
3. Contrapositive:
The contrapositive of a conditional statement flips and negates both the antecedent (P) and the consequent (Q).
Negating P: I did not receive a detention
Negating Q: I arrived at school on time
Contrapositive A: If I arrived at school on time, then I did not receive a detention.
Remember, when dealing with conditional statements, it is important to apply the correct logical operations to obtain the inverse, converse, and contrapositive.