Question

what is the contradiction of statement "m or n is even"?

Answer 1

neither (m or n is even), m and n are odd

Answer 2

oh.. what about the contrapositive statement for "m and n are both odd"?

Answer 3

contrapositive, as far as i can recall, relates to an if-then statement, a conditional statement

Answer 4

if p then q

contraPs to: if notq then notp

Answer 5

yep.. the original statement is "if m*n is even, then m or n is even" ...

Answer 6

that makes more sense :)

Answer 7

if m*n is even, then m or n is even

if -(m or n is even), then -(m*n is even)

if (m and n are odd), then (m*n is odd)

Answer 8

(2n+1)(2k-1)

(4nk +2k -2n) -1

2(2nk +k -n) -1

2m -1 is odd

Answer 9

thanks:) this helped a lot.. i
m actually preparing for an exam and i bumped into this question...

I didn't know what to do cause before, i bumped into a similar statement...

the Q statement says "then m and n are both even or m and n are both odd" ...

its contrapositive statement is "m or n is odd/even" ... i didn't know which one to use... XD

Answer 10

yeah, i tend to believe that reading shouldnt be required for math

Answer 11

-[ (m and n are both even) or (m and n are both odd)]

-(m and n are both even) and -(m and n are both odd)

(m or n is odd) and (m or n is even)

then either m or n is odd, but not both at the same time. I believe thats an exclusive OR construct that is difficult to get across in words