Final answer:
To prove that AQDA ∪ UAD = DA, we need to show that both sets contain the same elements. By breaking down the given sets and simplifying, we can conclude that AQDA ∪ UAD is equivalent to DA.
Step-by-step explanation:
To prove that AQDA ∪ UAD = DA, we need to show that both sets contain the same elements.
Let's break down the given sets:
QD U A: This set includes all elements in QD and all elements in A.
2QDA ∪ UAD: This set includes all elements in 2QDA and all elements in UAD.
Using set theory principles, we can rewrite AQDA ∪ UAD as (QD U A) ∪ (2QDA ∪ UAD), since AQDA can be broken down into QD and A.
Now, let's simplify:
(QD U A) ∪ (2QDA ∪ UAD) = QD U A U 2QDA U UAD
Since UAD is part of the given set, we can simplify further: QD U A U 2QDA U UAD = QD U A U 2QDA U UAD UDA UDA
Next, we combine similar terms: QD U 2QDA U UDA
Finally, we can rewrite this set as DA since QD and 2QDA are subsets of DA.
Therefore, AQDA ∪ UAD = DA
Considering the given sets QD U A and 2QDA ∪ UAD, you are tasked with proving that AQDA ∪ UAD=DA. Construct a logical and step-by-step proof to demonstrate that AQDA ∪ UAD is equivalent to the set DA based on the provided information.
Given: QDUA and 2QDA UAD
Prove: AQDA ∪ UAD=DA