A+B'C to standard minterm form

A standard (canonical) minterm form has all variables in every term. Here the variables are A, B, C.

Step 1: expand each term with the missing variables using $X + \overline{X} = 1$.

Term $A$ (B and C missing):

$$\begin{aligned} A &= A(B+\overline{B})(C+\overline{C}) \\ &= ABC + AB\overline{C} + A\overline{B}C + A\overline{B}\,\overline{C} \end{aligned}$$

Term $\overline{B}C$ (A missing):

$$\overline{B}C = \overline{B}C(A+\overline{A}) = A\overline{B}C + \overline{A}\,\overline{B}C$$

Step 2: add the terms and keep the repeated one only once ($A\overline{B}C$ appears twice; $X + X = X$):

$$F = ABC + AB\overline{C} + A\overline{B}C + A\overline{B}\,\overline{C} + \overline{A}\,\overline{B}C$$

Step 3: write the minterm numbers

$$F = A + \overline{B}C = \Sigma m(1,4,5,6,7)$$

Check: F = 1 whenever A = 1 (rows 4 to 7) or when B = 0, C = 1 (rows 1 and 5), which gives the same set.