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

Sure, let's solve the boolean expression step by step:

Given expression: (p∧¬q)+(p∧q)∧q

Step 1: Apply the distributive law to the expression. The distributive law states that A + BC = (A + B) (A + C). However, in this case, the distributive law cannot be applied as the expression is not in the form of A + BC.

Step 2: Apply the law of absorption. The law of absorption states that A + AB = A. However, in this case, the law of absorption cannot be applied as the expression is not in the form of A + AB.

Step 3: Apply the law of idempotence. The law of idempotence states that A + A = A and A.A = A. However, in this case, the law of idempotence cannot be applied as the expression is not in the form of A + A or A.A.

Step 4: Apply the law of complementation. The law of complementation states that A + A' = 1 and A.A' = 0. However, in this case, the law of complementation cannot be applied as the expression is not in the form of A + A' or A.A'.

Step 5: Apply the law of double negation. The law of double negation states that A'' = A. However, in this case, the law of double negation cannot be applied as the expression does not contain any double negation.

Step 6: Apply the law of De Morgan. The law of De Morgan states that (A + B)' = A'.B' and (A.B)' = A' + B'. However, in this case, the law of De Morgan cannot be applied as the expression is not in the form of (A + B)' or (A.B)'.

So, the given expression (p∧¬q)+(p∧q)∧q cannot be simplified further using the boolean laws. The expression remains as it is.