Econ: True or False and Why?

Question

For three commodity bundles X, Y and Z if X is at least as good as Y, Y is at least as good as X, and X is strictly preferred to Z, then , then Y is strictly preferred to Z.

i'm getting conflicting answers to this... and it doesn't make sense to me. what exactly does "at least as good as" mean? does it mean they are equal? or does it mean that you have to look at different cases (and by that i mean look at when x>y or y>x because my notes say x>~y is the same as x>y or x~y???)

the >~ sign is together for "at least as good as"

Answer 1

"at least as good as" means either equal or better than. In your case X is either equal or better than Y and vice versa meaning x and y are equal. that being the case if X is strictly preferred to Z then so is Y.

The answer is True.

Answer 2

NO THIS ANSWER IS TRUE

if X is greater than OR equal to Y  

AND

Y is greater than OR equal to X  

it must be that X=Y  

something at least as good as means it is greater than or equal to

so if X is greater (preferred) to Z  then Y is greater than (preferred) to Z

I think the others are confused about the first two statements