okay we need to talk about the problems uh for associated with lecture four so those two problems uh will be as follows uh problem for 0.1 will be the following um which of the following expressions is equivalent to a prime B or C or the ended with a prime B or d and the choices will be the choice a will be a prime or D Choice B is B or D Choice C is a prime B and choice d is a prime b or d so you should choose one of those Expressions is is the equivalent of this expression here a prime B or C or D ended with a prime b or d and when I mean when I say equivalent I mean always equal to the same value for any choice of values of the Boolean variables and problem for 0.2 is the same kind of problem which of the following expressions is equivalent to a prime or B or C Prime ended with a prime or C prime or D ended with B Prime or D Prime and the choices this time we a prime or C Prime ended with B Prime or D Prime B a or c ended with B chord d C a prime or D Prime ended with B Prime or C Prime and the final choice for this problem will be a prime or c ended with B Prime or D so those are the two problems for lecture four and one last hint I would like to give you is the following you should try to solve these two problems through the process of simplification and using the theorems that we discussed in the lecture however if you get stuck the hint is the following two expressions are equivalent if and only if they have the same truth table so if you wished you could approach these two problems from the point of view of constructing the truth tables for the given expressions and then the truth tables for your four choices uh but that would be a tedious way to solve these two problems it would be better to try to multiply these Expressions out and then use what we've learned uh during the lecture to simplify uh those expressions so good luck