Consider the following theorem.
Theorem: For all sets A and B, if A ⊆ B, then A ∪ B ⊆ B.
Su...
![Mathematics](/tpl/images/cats/mat.png)
Mathematics, 01.05.2021 18:30, Brucechavez3334
Consider the following theorem.
Theorem: For all sets A and B, if A ⊆ B, then A ∪ B ⊆ B.
Supply explanations for the steps in the proof of the theorem.
Proof:
Statement Explanation
Suppose A, B, and C are any sets such that A ⊆ B. starting point
We must show that A ∪ B ⊆ B. conclusion to be shown
Let x be any element in A ∪ B. start of an element proof
Then x is in A or x is in B. ---Select---
In case x is in A, then x is in B ---Select---
In case x is in B, then x is in B. tautology (p → p)
So in either case, x is in B. proof by division into cases
Thus every element in A ∪ B is in B. since x could be any element
of A ∪ B
Therefore, A ∪ B ⊆ B [as was to be shown]. ---Select---
![answer](/tpl/images/cats/otvet.png)
Answers: 3
Other questions on the subject: Mathematics
![image](/tpl/images/cats/mat.png)
Mathematics, 21.06.2019 16:30, mimithurmond03
Question 5 spring semester final exam math evaluate
Answers: 2
![image](/tpl/images/cats/mat.png)
Do you know the correct answer?
Questions in other subjects:
![Konu](/tpl/images/cats/geografiya.png)
Geography, 05.06.2020 19:04
![Konu](/tpl/images/cats/mat.png)
![Konu](/tpl/images/cats/mat.png)
![Konu](/tpl/images/cats/istoriya.png)
![Konu](/tpl/images/cats/mat.png)
Mathematics, 05.06.2020 19:04
![Konu](/tpl/images/cats/geografiya.png)
Geography, 05.06.2020 19:04
![Konu](/tpl/images/cats/en.png)
![Konu](/tpl/images/cats/mat.png)
Mathematics, 05.06.2020 19:04
![Konu](/tpl/images/cats/ekonomika.png)