# Why does Figure 2.F.1(b) (MWG page 30) satisfy the WARP (Definition 2.F.1)?

I can see that Figure 2.F.1(a) satisfies the WARP (Definition 2.F.1) in MWG (page 30). However, as the choice $$x(p',w')$$ is only feasible under the price-income level $$(p',w')$$ and $$x(p'',w'')$$ is only feasible under $$(p'',w'')$$ in Figure 2.F.1(b), why does it still satisfy the WARP definition which requires that a choice (say, $$x(p',w')$$) should be feasible under two different price-income levels (say, $$(p',w')$$ and $$(p'',w'')$$)?

Intuitively, this just says that if the bundle you choose was possible under wealth $$w$$ and price $$p$$ but it is not $$x(p, w)$$, then it must be that you cannot obtain it when price is $$p'$$ and wealth is $$w'$$.
It simply does not say anything about case (b) in which $$p' \cdot x(p'', w'') > w$$ and $$p'' \cdot x(p', w') > w''$$. Since the first part of the if ... then statement in the definition is false, everything evaluates to true.
• The definition is correct. Let's say the definition is "a demand function satisfies WARP if ($x$ and $y$ then $z$)". I was just saying that figure (b) also fits into the definition since $x$ (in figure (b)) is false, so the hole thing evaluates to true. – Art Nov 8 '19 at 1:36