Use Venn diagram to prove this logic equivalence functions (x+y).(x+y+z)=x+y?

To prove this logic equivalence using a Venn diagram, we can represent the left-hand side of the equation (LHS) as the intersection of two sets: (x+y) and (x+y+z).

Let's represent the set (x+y) as a circle labeled A, and the set (x+y+z) as a larger circle labeled B. The intersection of these two sets, represented by the LHS of the equation, is the area where the circles A and B overlap.

Now, let's consider the right-hand side of the equation (RHS), which is x+y. We can represent this set as a circle labeled C.

If we compare the Venn diagram representations of the LHS and RHS, we can see that the area where circles A and B overlap (LHS) is the same as the area covered by circle C (RHS). This shows that the two sides of the equation are equivalent.

Therefore, using a Venn diagram, we have proven that (x+y).(x+y+z) = x+y.