Why does /testfor @e[hasitem={item=air}] not allow you to check for players without a item within their inventory?

i am trying to make a minecraft map and i have to check if the player has nothing in their 12th and 16th slot and so i put this in the command block

/testfor @e[hasitem=\{item=air,location=slot.inventory,slot=11}]

but for some reason this doesnt work i think @e[hasitem=\{item=air}] should work for players lacking a item in their inventory because i see no reason for it not to