Using diagrams to prove logical equalities

[sumaiyakhatun27]

Let's look at how the Euler diagram is applied using the example of proving logical equality.

Using diagrams to prove logical equalities
Using diagrams to prove logical equalities
Let's imagine that we have a conjunction of sets A ∧ B.

First, we work with the left side of the equality. We need to use the Euler diagram lebanon mobile database to construct sets A and B, shade both circles with color, and thus highlight the disjunction.

Next, we need to show the inversion by shading the area outside these sets.

Now we switch to the right side of the equality. First, we show the inversion of this set with colored shading outside the circle A.

We perform the same action for set B.

We shade all intersection areas in black and obtain a graphical representation of the conjunction of the inversions of sets A and B.

Comparing the areas representing the right and left parts of the equality, we are convinced that they are equal. Thus, the truth of logical equality is proven using the Euler diagram.