$Y = A+\bar{B}C $

Perform double inversion on both sides,

We know

$\overline { \overline{Y}} =Y$,

Thus,$Y=\overline{\overline{A+\bar{B}C}}$

By DeMorgan's Laws,

NOTE:

$\overline{X+Z}=\bar{X}\times\bar{Z}$ and $\overline{X \times Z}=\bar{X}+\bar{Z}$

Thus,we get:

$Y=\overline{\bar{A}\times\overline{\bar{B}C}}$

$Y = \overline{\bar{A}\times(\overline{\bar{B}}+\bar{C})}$

$Y = \overline{\bar{A}\times(B+\bar{C})}$

$Y = \overline{\bar{A}}+\overline{B+\bar{C}}$

$Y = A+\overline{B+\bar{C}}$

Again taking double inversion;

$Y = \overline{\overline{A+\overline{B+\bar{C}}}}$

We can …