If $U=\{1,2,3,4,5,6,7,8,9\}, A=\{2,4,6,8\}$ and $B=\{2,3,5,7\}$. Verify that
(i) $(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$
(ii) $(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$

Answer

Related Courses

Algebra

Discussion

You must be signed in to discuss.

Top Algebra Educators

Watch More Solved Questions in Chapter 1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Video Transcript

Universal Said is given one coma to coma three comma for comma five comma six 78 common nine. And given equals to comb a pool, coma sixth eight and said be equal to two comma three comma five comma seven. So in part first we have to verify that compliments of mm the union be equal to compliments of side A intersection compliments of B. Therefore we find a union be. So here we can said two common three comma four. Come on five comma six coma seven comma eight. Now we find compliments of set a union be equal to one common name. Because here we know that compliments of a union be equal to Universal said minus mm. Union be two E. Intersection B. So here we get common elements which is only two. So we can find compliments of said A intersection B. So here we get one coma three comma for comma five comma six, comma seven comma eight. Human nine now is sold part second compliment offset E. Intersection B. Equal to compliments of say E. Union complement of side B. So first of all we find the intersection E. B. Equal to we get to no complement of a intersection B. Yes. Universal said minus E. Intersection B. So here we get one coma three coma five coma full comma six coma seven koma eight. Common name. No. We find compliments of say A union compliment outside B. Equal to one comma three. I don't fly coma 77 Come on nine. A. Union one coma four coma six koma 8 to 9 equal to one comma three comma full coma wife comma six comma seven from eight common nine. So here you can see that compliments of a intersection B. Equal to complement of said E. Union complement of side B. It is verified. So it is our final answer.

We have video lessons for 83.41% of the questions in this textbook