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moongazer
What is the meaning of "converse" and "inverse" in Math?
It has something to do with logic
converse: q -> p the hypothesis and the conclusion switch places -- the conclusion becomes the hypothesis, the hypothesis becomes the conclusion.. inverse: not p -> not q negate both the hypothesis and the conclusion
converse of a statement that says "if P then Q" is the statement "if Q, then P"
contrapositive (a combination of the converse and the inverse): not q -> not p negate and switch the hypothesis and the conclusion..
converse: If I am in China, then I am in Bejing. (The conclusion and hypothesis have switched places. Notice that the converse of a true conditional statement is not guaranteed to be true.)
for example, converse of "if \(x=3\) then \(x^2=9\)" is "if \(x^2=9\) then \(x=3\) first statement is true, second is false, which means the converse of a statement is not logically equivalent to the statement
inverse: If I am not in Bejing, then I am not in China. (Like the converse, the inverse of a true condition may not always true.).
contrapositive: If I am not in China, then I am not in Bejing. (Note: If the conditional statement is true, the contrapositive will always be true too.)
converse is when you switch them. like girls who wear converse sneakers when the play basketball the ball makes a swoosh sound when it goes in. so think converse swoosh and swoosh sounds like switch.
i always think converse and inverse in logic is backwards
inverse to me is an undoing; so q -> p would make sense; but its not lol
So if the statement says "All pairs of vertical angles are congruent angles." the inverse will be: "All pairs of angles that are not vertical angles are not congruent angles." and the converse is: "All pairs that are congruent angles are vertical angles." and the contrapositive is: "All pairs that are not congruent angles are not vertical angles." Is this correct?
can you form that into an if then statement?
if "a pair of angles are vertical", then "they are congruent" looks to be a good mock up of it ...
so yeah, that looks good
How about this? So if the statement says "All pairs of vertical angles are congruent angles." the inverse will be: "If All pairs of angles are not vertical angles, then all pairs of angles are not congruent." and the converse is: "If all pairs of angles are congruent, then all pairs of angles are vertical." and the contrapositive is: "If all pairs of angles are not congruent, then all pairs of angles are not vertical."
yep, inverse negates, converse swaps, and contraP negates and swaps