Question

Need help with contrapositive. See posted math notation.

Answer 1

\[For R \subseteq A \times A\]
\[[(a,b) \in R \wedge (b,a) \in R] \implies a = b\]

I need to find the contrapositive.

Answer 2

Contrapositive: negate both statements, change the direction of the implication.

Answer 3

yes, i am aware, but all the notation is confusing to me how to negate.

Answer 4

so a is not equal to b implies .... lost here

Answer 5

Can I assume there's no issue with negation of a=b?

Answer 6

Okay cool.

Answer 7

negation of (a^b) is ~a or ~b

Answer 8

\[(a,b) \notin R \wedge (b,a) \not R\] ?

Answer 9

negation of a = b is a != b

Answer 10

That first part reads thusly:
[(a,b)∈R∧(b,a)∈R]
if (a,b) is an element of R AND (b,a) is an element of R

Answer 11

yes. so i am thinking leave the AND as turn to not in R?

Answer 12

Almost, Sean. But the and sign becomes an or sign.
Think about the negation of a statement like
I am tall and male. That statement is false if I am short, but it's also false if I'm female. I don't have to be short AND female for it to be false.

In general, negation of (a and b) is (not a or not b)

Answer 13

ok. so something like this:

Answer 14

\[a \neq b \rightarrow [(a,b) \notin R \vee (b,a) \notin R]\]

Answer 15

word

Answer 16

yussss

Answer 17

thanks guys. hope i can give you both good answer.