moongazer
  • moongazer
What is the meaning of "converse" and "inverse" in Math?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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moongazer
  • moongazer
It has something to do with logic
anonymous
  • anonymous
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
anonymous
  • anonymous
converse of a statement that says "if P then Q" is the statement "if Q, then P"

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anonymous
  • anonymous
contrapositive (a combination of the converse and the inverse): not q -> not p negate and switch the hypothesis and the conclusion..
anonymous
  • anonymous
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.)
anonymous
  • anonymous
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
anonymous
  • anonymous
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.).
anonymous
  • anonymous
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.)
anonymous
  • anonymous
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.
amistre64
  • amistre64
i always think converse and inverse in logic is backwards
amistre64
  • amistre64
inverse to me is an undoing; so q -> p would make sense; but its not lol
moongazer
  • moongazer
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?
moongazer
  • moongazer
Anyone?
amistre64
  • amistre64
can you form that into an if then statement?
moongazer
  • moongazer
ok
amistre64
  • amistre64
if "a pair of angles are vertical", then "they are congruent" looks to be a good mock up of it ...
amistre64
  • amistre64
so yeah, that looks good
moongazer
  • moongazer
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."
amistre64
  • amistre64
yep, inverse negates, converse swaps, and contraP negates and swaps
moongazer
  • moongazer
Thanks :)

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