Question

Mooooore contrapositives. .-.

Answer 1

If y is greater than 3, then y does not equal 4.
I know that the contrapositive would start out as
"If y equals 4," but I have no idea what to do with the greater than symbol thingy.

Answer 2

say it is not greater than 3

Answer 3

What would that look like? This?

Answer 4

yes

Answer 5

or != or <>

Answer 6

\[
\neg (x\gt y) \iff x\leq y
\]

Answer 7

\[
\neg (x\gt y) \iff x=y\lor x\lt y\iff x\leq y
\]

Answer 8

All these symbols are confusing me. o-O

Answer 9

So just put a slash through the inequality symbol, right?

Answer 10

@ganeshie8

Answer 11

`If y is greater than 3, then y does not equal 4. `

your given statement is in words or symbols ?

Answer 12

statement : if \(y \gt 3\), then \(y \ne 4\)

like this ?

Answer 13

Yes. ^.^

Answer 14

then you're absolutely right!
just swap and negate

Answer 15

statement : if \(y \gt 3\), then \(y \ne 4\)

contrapositive : if \(y = 4\), then \(y \not \gt 3\)

Answer 16

thats technically correct, but doenst that look ugly ?

Answer 17

Yeah, it looks strange, that's why I was confused. xD

Answer 18

we may replace \(\not \gt\) by the familiar and cute symbol \(\le \)

Answer 19

contrapositive : if \(y = 4\), then \(y \le 3\)

see if this looks good

Answer 20

saying you are "not taller" than me is

same as saying

you're "below or equal to" my height

Answer 21

Ah, true.
Thanks!! \(\Large\color{magenta}{\heartsuit}\)

Answer 22

np :)