Not every transitively D-space is D

In 2008, Liang-Xue Peng defined a weakening of the D-space property known as the transitively D property. He asked whether or not every transitively D-space is D. We show that three different examples of linearly Lindelöf, non-Lindelöf spaces are transitively D but not D, answering Peng's question in the negative.