(p∧¬q)+(p∧q)∧q solve the boolean expression

To solve the Boolean expression, we can use the laws of Boolean algebra. Here are the steps:

1. Simplify the expression within the brackets first:

   (p∧¬q) + (p∧q)∧q

2. According to the law of idempotence (p∧q)∧q simplifies to p∧q:

   (p∧¬q) + p∧q

3. Now, we can apply the distributive law, which states that A + BC = (A + B)(A + C). So, we get:

   p∧(¬q + q)

4. The expression ¬q + q is a law of excluded middle, which means it will always be true (1). So, the expression simplifies to:

   p∧1

5. According to the identity law, anything AND 1 is itself, so the final simplified Boolean expression is:

   p