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In this problem we prove the following statement Let A B be sets in a...

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Basic Math

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In this problem we prove the following statement Let A B be sets in a universe U Then An Bc C 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 A n B Then x E A and x E B by justification Since a A this means that x A by justification Using the same reasoning a E B means that a B so x EB is true Combining these facts A EB is true Therefore EA V EB is true using justification In other words E AUB is true using justification Since AUB this means that a E AUB using justification 9 I So x A is true which is equivalent to x AUB

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