Question #11...

[Cristian De Leon]

I know we went over #11 of the practice exam in class, but I think that the way that it was explained in class was incorrect.

I believe that the way that it was explained in class was that (92.....91)x(29....71) is not congruent 2(mod10) because 

(92....91) is congruent 2(mod10)  is equal to 1... and that (29....71) is congruent 2(mod10) is equal to 1..

and that 1x1 =/= 2

...can anyone confirm this? there's a chance that i might have written it down incorrectly

any who.. 

the way that i propose also makes use of theorem 5 p.242

(92.....91)x(29....71) is not congruent 2(mod10) because

(92....91) is congruent 2(mod10)  says ((92....91)-2) is divisible by 10 by definition 3 page 240

I claim this is false..

... and that (29....71) is congruent 2(mod10) says ((29....71)-2)) is divisible by 10 by definition3 page240

which is also false...

Going back to the theorem.. is says that both of these congruence statements must be true

and using our universal quantifier..

F and F is    False

Can anyone verify this?

I apologize if I confused anyone or if I misunderstood the in-class explanation

Best of luck on the midterm!

-Cris De Leon

[Kevin Lin]

Theorem 3 on page 241 shows that the two different definitions/notations are actually equivalent.