Equivalence of premises

Question

I have a question related to truth tables and Boolean Algebra.

I have the following premises and I am asked to check if they are the same by applying the truth tables. To do this, I considered the product of the variables involved as the conjunctor ^ (and) and solved the equivalence by applying truth tables.

x¬y + y¬z + ¬xz = ¬xy + ¬yz + x¬z

Therefore, after these changes I have obtained the following premises, which I have been able to validate that the truth tables are the same, but I do not know if the method of transformation of the premises is correct.

$${{(x\land\lnot y)} \land {(y\land\lnot z)} \land {(\lnot x\land z)}} = {{(\lnot x\land y)} \land {(\lnot y\land z)} \land {(x\land\lnot z)}}$$

Answer 1

The product is conjunction, the sum is disjunction.

$x¬y + y¬z + ¬xz = ¬xy + ¬yz + x¬z$

You are testing whether this holds:

$${{(x\land\lnot y)} \lor {(y\land\lnot z)} \lor {(\lnot x\land z)}} = {{(\lnot x\land y)} \lor {(\lnot y\land z)} \lor {(x\land\lnot z)}}$$