I:$2-33$ Dependency Requirements. John and Carole file a joint return and have three children:

Jack, David, and Kristen. All three children live at home the entire year. Below is informa$-$tion about each of the children for $2023$:

$$ Jack $($age $23)$: graduated from college last year and will start medical school next year.

This year, Jack worked sparingly as he studied for the medical school entrance exam,

but did earn $$5,000.$ John and Carole provided $80\%$ of Jack$$s support during the year.

$$ David $($age $20)$: a full$-$time student at State U$.,$ earned $$6,400$ from a part$-$time job, and

provided $40\%$ of his own support.

$$ Kristen $($age $15)$: a full$-$time student in high school, had no gross income, and provided

none of her own support.

a$.$ Based on the above facts, which of the children can be claimed as dependents by John

and Carole this year?

b$.$ How would your answer to Part a change if Jack began medical school in August of

this year?

c$.$ How would your answer to Part a change if Jack earned $$3,000$ rather than $$5,000?$

d$.$ How would your answer to Part a change if David was a part$-$time student rather than

a full$-$time student?

e$.$ How would your answer to Part a change if David provided $60\%$ of his own support

rather than $40\%?$