Question #144633
Let A = {n ∈ Z | n = 5r for some integer r} and B = {m ∈ Z | m = 20s for some integer s}.
a. Is A ⊆ B? Explain.
b. Is B ⊆ A? Explain
1
Expert's answer
2020-11-17T07:37:37-0500

Let A={nZ  n=5r for some integer r}A = \{n\in\mathbb Z\ |\ n = 5r\ \text{for some integer}\ r\} and B={mZ  m=20s for some integer s}B = \{m\in\mathbb Z\ |\ m = 20s\ \text{for some integer}\ s\}.


a. Since n=5=51n=5=5\cdot1 and 1Z,1\in\mathbb Z, we conclude that n=5An=5\in A. On the other hand, n=520sn=5\ne20\cdot s for each integer ss, and therefore, n=5Bn=5\notin B. We conclude that it is not true that AB.A\subseteq B.


b. If mBm\in B then m=20sm = 20s for some integer ss. It follows that m=5(4s),4sZm=5(4s), 4s\in\mathbb Z, and consequently, mAm\in A. Therefore, BA.B\subseteq A.



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS