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moongazer

What is the meaning of "converse" and "inverse" in Math?

  • one year ago
  • one year ago

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  1. moongazer
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    It has something to do with logic

    • one year ago
  2. AcidRa1n
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    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

    • one year ago
  3. satellite73
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    converse of a statement that says "if P then Q" is the statement "if Q, then P"

    • one year ago
  4. AcidRa1n
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    contrapositive (a combination of the converse and the inverse): not q -> not p negate and switch the hypothesis and the conclusion..

    • one year ago
  5. AcidRa1n
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    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.)

    • one year ago
  6. satellite73
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    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

    • one year ago
  7. AcidRa1n
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    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.).

    • one year ago
  8. AcidRa1n
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    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.)

    • one year ago
  9. jakezz
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    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.

    • one year ago
  10. amistre64
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    i always think converse and inverse in logic is backwards

    • one year ago
  11. amistre64
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    inverse to me is an undoing; so q -> p would make sense; but its not lol

    • one year ago
  12. moongazer
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    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?

    • one year ago
  13. moongazer
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    Anyone?

    • one year ago
  14. amistre64
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    can you form that into an if then statement?

    • one year ago
  15. moongazer
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    ok

    • one year ago
  16. amistre64
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    if "a pair of angles are vertical", then "they are congruent" looks to be a good mock up of it ...

    • one year ago
  17. amistre64
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    so yeah, that looks good

    • one year ago
  18. moongazer
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    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."

    • one year ago
  19. amistre64
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    yep, inverse negates, converse swaps, and contraP negates and swaps

    • one year ago
  20. moongazer
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    Thanks :)

    • one year ago
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