Here's a very simplified approach. All you have to do is observe.
The function $F$ is true when B and C are 0.
$A$ is true, when B and C are 1.
$\overline{A}$ is true, when B is 1 and C is 0.
Make K-map of three variables. (8 cells)
Where B and C are 0, put 1 in that cell irrespective of what A is.
Where B and C are 1, put 1 in the cell against A.
Where BC = 10, put 1 in the cell against $\overline{A}$, ie, where A is 0.
This is the K-map you'll get.
Image source: https://pyq.ravindrababuravula.com/gate-1992/ques?questionid=2157&quiz_name=Gate-1992
$F = ABC+\overline{B} \overline{C}+\overline{A} \overline{C}$