Please simplify $((p \land f) \lor q) \land t$ and prove correctness of your simplification.

Question

I'm trying to simplify this expression, and I got the following:

$$((p \land f)\lor q) \land t= (((p\land f)\lor q)\land t) =(t \land (p\land f))\lor (q\land t)$$

would this be the simplified version. I'd appreciate some explaining. Thanks

Answer 1

I'm trying to simplify this expression, and I got the following:

$$((p \land f)\lor q) \land t ~{=~ (((p\land f)\lor q)\land t) \\ =~(t \land (p\land f))\lor (q\land t)}$$

would this be the simplified version. I'd appreciate some explaining. Thanks

That is okay.   Whether this is simpler or not is debatable, as you have increased the count of literals and operators.   However, you have reduced the depth of nesting and arrived at the Distributed Normal Form:   $(p\wedge f\wedge t)\vee (q\wedge t)$

You can also easily put it into the Conjunctive Normal Form:   $(p\vee q)\wedge (f\vee q)\wedge t$

It is a matter of perspective, but there is a certain elegance to the Normal Forms, and they are at least easy to compare and evaluate.