In this lecture we will present several useful tautologies. Laws of Equivalence Equivalence has a dual role.
Any expression is equivalent to itself.
If E1 is equivalent to E2 and E2 is equivalent to E3 then E1 is equivalent to E3. Two expressions are equivalent if and only if their negations are equivalent. In a sum of products we can eliminate any product that has a superset of the literals in another product. Finally we use the law of double negation p'' p to remove any double negations in the expression. Duality Notice that our laws can be grouped into pairs such that, in each pair, the roles of AND and OR are interchanged.