question about equivalence of boolean statements Does the function $(p \land q) \lor r$ equal the function $p \land (q \lor r)$?
please it would be suitable if in your feedback you will include which algebraic rule for boolean function to follow..
Thanking you in anticipation.

$$(p \land q) \lor r\equiv (p\lor r) \land (q\lor r)\tag{1}$$
$$p\land (q\lor r) \equiv (p\land q) \lor (p \land r)\tag{2}$$
In both cases, I applied a distributive law/rule. 
To see more vividly that the two statements are not equivalent, take $p$ to be false, $r$true.  Then: Is statement $(1)$ true of false? What about statement $2$?
