Find the Conjunctive normal for and Disjunctive normal form ofgiven Boolean function f(x, y, z)=(xvy) (xvz).

Alright, let's break this down. We're dealing with a Boolean function, which is a fancy way of saying we're working with true or false values. In this case, we're working with the variables x, y, and z.

The function we're given is f(x, y, z) = (x v y) (x v z). The "v" symbol stands for "OR", which means at least one of the variables has to be true for the whole statement to be true.

Step 1: Let's find the Conjunctive Normal Form (CNF). This is a way of writing the function where we have a bunch of "AND" statements grouped together.

First, we distribute x over y and z. This gives us:

f(x, y, z) = x v (y and z)

This is the Conjunctive Normal Form.

Step 2: Now, let's find the Disjunctive Normal Form (DNF). This is a way of writing the function where we have a bunch of "OR" statements grouped together.

We can rewrite the function as:

f(x, y, z) = (x and y) v (x and z)

This is the Disjunctive Normal Form.

So, in simpler terms, the CNF is like saying "I'll go to the park if it's sunny and (it's the weekend or I have no homework)". The DNF is like saying "I'll go to the park if (it's sunny and it's the weekend) or (it's sunny and I have no homework)".