1 2 points For each of the following assertions state whethe

1. (2 points) For each of the following assertions, state whether it is true or false. (No justification is necessary.)

(i) (aZ)(bZ)a+b=5. (ii) (aZ)(bZ)a+b=5.

(ii) (aZ)(bZ)a+b=5. (iii)

(iii) (mZ)(nZ) (2n=m)or(2n+1=m) .

(iv) nZsuchthat n2 N = (2+3=4).

Please do all of them .. this is a proof math cours

Solution

i)

True

Choose. b=5-a for any a in Z

ii)

False

Assume true. So such an a exists

a+0=5

Hence, a=5

a+5=5

Hence, a=0

Hence contradiction

SO no such a exists

iii)

True

Case 1. m even

m=2n for some integer n

Case 2. m is odd

m=2n+1 for some intger n

Hence, proved

iv)

False

-n^2 <0 for all n in Z

But N has only positive integers