 In this video, we provide the solution to question number eight for practice exam number four for math 1030 We're given two sets a and b such that the card Nality of B is 14 The card Nality of a Union B is 67 and the inters the card Nality of the intersection of a A intersect B is 10 we want to find the card Nality of a so by the inclusion exclusion formula We have that the card Nality of the Union is equal to the card Nality of a plus the card Nality of B Minus the card Nality of the intersection So we know a lot of these numbers here, so the Union has a size of 67 We don't know a that's what we're looking for here. We know B is 14 and We know the intersection is 10 so simplifying the right hand side 14 take away 10 gives us 4 and so then we're going to subtract 4 from both sides of the equation right here and so we get that the card Nality of a Is going to equal 67 minus 4 which then gives us 63 and so we see that the correct answer is in fact D