All Asatru are Heathens...?

All Asatru are Heathens therefore all Heathens are Asatru

correct?

Not correct. Asatru could be a subset of Heathens.

Incorrect. There are many types of Germanic/Nordic Heathens. Some of us reject any title other than Heathen or Germanic/Nordic Heathen, period. In my Kindred, we're like the non-denominational christian churches and have members ranging from Asatruar to Theodists to Forn Si?r and others.

There are also Heathens who are not of a Germanic/Nordic persuasion and who would therefore most likely feel no connection to the Aesir or Vanir. It would make no sense to refer to them as "Asatru" since the name itself refers to those who are "true to the Aesir".

Nope.

Asatruars are Heathen, but not all Heathens are Asatru. Asatru is basically Norse Heathenry.

No. All Asatru are Heathen, but not all Heathen are Asatru. There are several other Heathen religions.

Not logical. All Asatru are indeed Heathens, but the following doesn't follow:

All cars have wheels therefore a bicycle is a car.

Nope.

All Baptists are Christians but not all Christians are Baptist.
All Wiccans are pagan, not all pagans are Wiccans.
All Asatru are Heathens but not all Heathens are Asatru.