is it true "Whenever a good is a Giffen good it has a positively-sloped demand curve"

Yes, it's true. A Giffen good is a special type of inferior good which defies the basic law of demand. The law of demand states that as the price of a good increases, the quantity demanded decreases, and vice versa, assuming all other factors remain the same. This results in a downward sloping demand curve.

However, a Giffen good has an upward sloping demand curve, which means that as the price of the good increases, the quantity demanded also increases. This is contrary to the law of demand.

The reason for this is that a Giffen good is so essential to a consumer (usually a low-income consumer) that they will continue to purchase it even when the price increases, often at the expense of purchasing other goods. This is a very rare occurrence and is typically associated with staple foods in very poor economies.

So, whenever a good is a Giffen good, it does indeed have a positively-sloped demand curve.