a) XX: Female, Fire Breathing
b) XY: Male, Non-Fire Breathing
c) XY: Male, Non-Fire Breathing
d) XXT: Female, Carrier for Fire Breathing
e) X*XT: Female, Fire Breathing
In dragons, fire breathing is a sex-linked trait, meaning that the gene for fire breathing is located on the X chromosome.
Females have two X chromosomes, while males have one X and one Y chromosome.
This means that females can be either homozygous dominant (X^fX^f), which means they have two copies of the fire breathing gene and are fire breathing, or heterozygous (X^fX^N), which means they have one copy of the fire breathing gene and one copy of the non-fire breathing gene and are carriers for fire breathing.
Males can only be non-fire breathing (X^NXY^N), as they need two copies of the fire breathing gene to be fire breathing, and they can only get one copy from their mother.
The image you sent shows the following:
a) XX: This dragon is a female, as she has two X chromosomes. She is also fire breathing, as the X chromosome with the fire breathing gene is marked with an "f".
b) XY: This dragon is a male, as he has one X and one Y chromosome. He is non-fire breathing, as the X chromosome with the fire breathing gene is marked with an "N".
c) XY: This dragon is a male, as he has one X and one Y chromosome. He is non-fire breathing, as the X chromosome with the fire breathing gene is marked with an "N".
d) XXT: This dragon is a female, as she has two X chromosomes. She is a carrier for fire breathing, as one X chromosome has the fire breathing gene (marked with an "f") and the other X chromosome has the non-fire breathing gene (marked with an "N").
e) X*XT: This dragon is a female, as she has two X chromosomes. She is fire breathing, as both X chromosomes have the fire breathing gene (marked with an "f").