annie said:q)give the converse ,the contrapositive and inverse of these conditional statements
a)if it rains today,then i will drive to work
b)if |x|=x then x>=0
c)if n is greater than 3,then n^2 is greater then 9
Plato said:If P then Q. What are the converse ,the contrapositive and inverse of that statement?
annie said:converse q then p
contrapositive not q then not p
inverse not p then not q
i don't understand how to do b part
Plato said:b) \(\displaystyle \text{If }|x|=x\text{ then }x\ge 0~.\)
Inverse: \(\displaystyle \text{If }|x|\ne x\text{ then }x< 0~.\)
Now you post the others.
NO!annie said:converse if x>=0 then |x|=x
contrapositive if x ne 0 then |x| ne x
The converse of a conditional statement is a statement that switches the hypothesis and conclusion of the original statement. For example, if the original statement is "If it is raining, then the ground is wet", the converse would be "If the ground is wet, then it is raining."
The contrapositive of a conditional statement is a statement that switches the hypothesis and conclusion of the converse statement and negates both. Using the same example as above, the contrapositive would be "If the ground is not wet, then it is not raining."
The inverse of a conditional statement is a statement that negates both the hypothesis and conclusion of the original statement. In contrast, the contrapositive negates both the hypothesis and conclusion of the converse statement. Using the same example, the inverse would be "If it is not raining, then the ground is not wet."
The original statement, its converse, and its contrapositive are all logically equivalent, meaning they have the same truth value. This means that if the original statement is true, then its converse and contrapositive will also be true, and if the original statement is false, then its converse and contrapositive will also be false.
In scientific research, the use of these logical statements can help in determining the validity of a hypothesis or theory. By examining the converse, contrapositive, and inverse of a statement, scientists can identify any potential flaws or contradictions in their reasoning, and make adjustments to their theories accordingly. This can lead to more accurate and reliable conclusions in scientific research.