why all chordates are vertebrates but all vertebrates are not chordates?

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http://www.neonaturalist.com/nature/chordates.html

To understand why all chordates are vertebrates but not all vertebrates are chordates, we need to break down the terms "chordate" and "vertebrate" and examine their definitions.

A chordate is a member of the phylum Chordata, which includes organisms that share certain characteristics at some point in their life cycle. These characteristics include having a notochord (a flexible, rod-like structure) at some stage, a dorsal hollow nerve cord, pharyngeal slits or pouches, and a post- tail.

On the other hand, a vertebrate is a specific subgroup within the chordates, characterized by the presence of a vertebral column or backbone. This bony or cartilaginous structure protects the spinal cord and provides support for the body.

So, why are all chordates vertebrates? This is because within the phylum Chordata, all organisms that possess a vertebral column and meet the characteristics of chordates are classified as vertebrates. In other words, vertebrates are a subset of chordates that have developed a backbone.

However, why is it not true that all vertebrates are chordates? This is because there exist a few specific vertebrate groups that have lost or modified some of the other defining characteristics of chordates. For example, the class of jawless fish known as hagfishes and lampreys still possess a vertebral column but lack other chordate characteristics like pharyngeal slits or the presence of a true notochord at all stages.

In summary, all chordates are vertebrates because vertebrates are a subset of the larger chordate group. However, not all vertebrates possess all the defining characteristics of chordates, making them exceptions to the general rule.