## moongazer 3 years ago What is the meaning of "converse" and "inverse" in Math?

1. moongazer

It has something to do with logic

2. AcidRa1n

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

3. satellite73

converse of a statement that says "if P then Q" is the statement "if Q, then P"

4. AcidRa1n

contrapositive (a combination of the converse and the inverse): not q -> not p negate and switch the hypothesis and the conclusion..

5. AcidRa1n

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.)

6. satellite73

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

7. AcidRa1n

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.).

8. AcidRa1n

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.)

9. jakezz

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.

10. amistre64

i always think converse and inverse in logic is backwards

11. amistre64

inverse to me is an undoing; so q -> p would make sense; but its not lol

12. 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?

13. moongazer

Anyone?

14. amistre64

can you form that into an if then statement?

15. moongazer

ok

16. amistre64

if "a pair of angles are vertical", then "they are congruent" looks to be a good mock up of it ...

17. amistre64

so yeah, that looks good

18. 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."

19. amistre64

yep, inverse negates, converse swaps, and contraP negates and swaps

20. moongazer

Thanks :)