In this problem we prove the following statement Let A B be

Last updated: 10/29/2023

In this problem we prove the following statement Let A B be sets in a universe U Then A n BC AUB Your task is to provide justification for some of the steps Possible answers are given below Put a number into each blank with no parentheses 1 definition of union 2 definition of intersection 3 definition of subset 4 definition of set subtraction i e S T 5 definition of complement 6 DeMorgan s law of logic Proof Let a An B Then x EA and a E B by justification 2 Since a A this means that a A by justification 5 Using the same reasoning a E B means that a B so x B is true Combining these facts x E A A B is true Therefore EA V E B is true using justification 6 In other words E AUB is true using justification 4 Since AUB this means that a AUB using justification 3 This concludes the proof that ABC AUB D So EA is true which is equivalent to a AUB