Question

Is the following formula satisfiable?

$(\mathbf{x}\vee \mathbf{y})\wedge (\mathbf{x}\vee \mathbf{y})\wedge (\mathbf{x}\vee \mathbf{y})\wedge (\mathbf{x}\vee \mathbf{y}).$

Short answer

This technique$XY\left(XVY\right)\left(X-VY\right)\left(X-VY-\right)$ satisfiable since it uses every one of the variables that produce true and pair values based on X and Y.

Step-by-step solution

Step 1:Satisfiable means

It implies that the level of $XandY$may be expressed in terms of True or False. This algorithm must yield one actual worth in just about any mixture of true and false. So, let's set the true and false combinations in the $XandY$positions.

Truth Table

$$\begin{gathered} True=T \\ and \\ False=F \\ X-isthebalanceoftheX \end{gathered}$$

Truth table approach:

$$\begin{gathered} XY\left(XVY\right)\left(X-VY\right)\left(X-VY-\right)\mathbf{Final}\mathbf{result} \\ \mathbf{T}\mathbf{}\mathbf{}\mathbf{T}\mathbf{T}\mathbf{T}\mathbf{F}\mathbf{F} \\ \mathbf{T}\mathbf{}\mathbf{}\mathbf{F}\mathbf{T}\mathbf{F}\mathbf{T}\mathbf{F} \\ \mathbf{F}\mathbf{}\mathbf{}\mathbf{T}\mathbf{T}\mathbf{T}\mathbf{T}\mathbf{T} \\ \mathbf{F}\mathbf{F}\mathbf{}\mathbf{}\mathbf{F}\mathbf{F}\mathbf{F}\mathbf{F} \end{gathered}$$

This ultimate method, which is really the As well as operations of the all the parameters, provides the True value for a pair of $X=FalsewithY=True$, hence the formula is satisfiable. However, it is not a tautology because it gives the erroneous value for some values