 Hi and how are you all today? Let us discuss this question. It says fill in the blank to make each of the following a true statement. Now these are the parts of the question which are given to us and in each we need to fill in the blank. Right? The first blank which says A union A complement. Let us have a universal set a very small universal set overhead and let this be set A. So set A is having all the elements in this and A complement means everything else in the universal set except what is there in A. So this plus this will give us the whole universal set. So the blank will be that A union A complement is equal to universal set whereas again this is the universal set this is set A. We have phi complement phi is a null set null sets complement means the universal set. Right? So universal set intersection A will give us what what will be the elements which are present in the universal set also and in set A also it will be set A itself. Right? So there we will be filling it with set A whereas A intersection A complement will be equal to phi it will be a null set because all the elements of A are different from all the elements of A complement and hence there is no intersection between them whereas A complement universal sets complement means whatever is present in the universal set and the elements which are outside this universal set and set A means the elements which are present in universal set. So there is no intersection between these two and hence the answer will again be equal to phi. So this completes the question that was given to us. You could have taken examples also to make your clearer more vision but if you do it by diagram it will be more clearer to you. Bye for now.