Question

4. Negate the following statements.
(a) 3x > 6 ________________________________
(b) All natural numbers are integers. ________________________________

Answer 1

a) \[3x \le 6\]b)there exist a number which is not integer

Answer 2

first answer is right..
negate of all is there

Answer 3

ok thank you

Answer 4

a) can be negated for the case of all x such that:
0<x<2

b) depends on your definitions, 0 might negate this, if it is counted as a natural number, but not an integer.

Answer 5

I'm sorry, a) should be:
For all x < 2

Answer 6

I thought it would be x>2 because you flip inequalities when they are negative?

Answer 7

Well, let's look at the case of x=-3

3(-3) > 6
-9 > 6 is false and therefore negates the claim
3x>6

This will hold true for all negatives, and 1,2 for x
So, the set of x such that
x<2
negates the original.

Answer 8

oh ok gotcha thanks