A logic circuit provides the output Y as per the following truth table :

A	B	Y
0 0 1 1	0 1 0 1	1 0 1 0

The expression for the output Y is

First, write down the given truth table clearly:

Identify the rows where the output $Y$ is **1**. They are:

• Row 1: $A\; =\; 0, B\; =\; 0, Y\; =\; 1$
• Row 3: $A\; =\; 1, B\; =\; 0, Y\; =\; 1$

For each such row write the corresponding minterm (product term) using the convention that a variable is complemented when its value is 0.

Row 1 gives the minterm $A̅·B̅$.
Row 3 gives the minterm $A·B̅$.

Combine the minterms with OR to obtain the sum‑of‑products (SOP) form:

$A̅·B̅\; +\; A·B̅$

Now simplify by factoring the common factor $B̅$:

$(A̅\; +\; A)·B̅$

Since $A̅\; +\; A\; =\; 1$ (a variable OR its complement is always true), the expression reduces to:

$1·B̅\; =\; B̅$

Thus the Boolean expression that matches the given truth table is simply the complement of $B$:

B̅

We can also verify the result directly from the table: whenever $B\; =\; 0$, $Y\; =\; 1$; whenever $B\; =\; 1$, $Y\; =\; 0$. This is exactly the behavior of $B̅$.