The discussion focuses on deriving the converse, contrapositive, and inverse of several conditional statements. For the statement "If it rains today, then I will drive to work," the converse is "If I drive to work, then it rains today," the contrapositive is "If I do not drive to work, then it does not rain today," and the inverse is "If it does not rain today, then I will not drive to work." The mathematical statement "If |x|=x, then x≥0" has the inverse "If |x|≠x, then x<0." The participants clarify these logical transformations, ensuring a comprehensive understanding of the concepts involved.
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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) $$\text{If }|x|=x\text{ then }x\ge 0~.$$
Inverse: $$\text{If }|x|\ne x\text{ then }x< 0~.$$
Now you post the others.
NO!annie said:converse if x>=0 then |x|=x
contrapositive if x ne 0 then |x| ne x