Question

Illustrate each of the following diagram:TRY HARDERNeed rn asap :)

Answer 1

We will draw the Venn diagram to show the universal st U and the 3 sets A, B, C

Now we will start with the common elements of A and B

5 is the common element of A and B

1 is the common element between A and C

2, 4, and 6 are the common elements between B and C

3 is in A only

Now we can answer the question using the Venn diagram

1. A' means all the elements in U except A, then

`A^(\prime)=\lbrace2,4,6\rbrace`

2. B U C means all elements in B and C

`B\cup C=\lbrace1,2,4,5,6\rbrace`

3. A intersect C means common elements in A and C

`A\cap C=\lbrace1\rbrace`

4. B' all elements in U not in B

`B^(\prime)=\lbrace1,3\rbrace`

5. A U B all elements in A and B

`A\cup B=\lbrace1,2,3,4,5,6\rbrace`

a. (A U C}' means all elements in U except A and C

`(A\cup C)^(\prime)=\lbrace\rbrace=\Phi`

Empty set because all elements are in A and C

b. A' intersects C'

`\begin{gathered} A^(\prime)=\lbrace2,4,6),C^(\prime)=\lbrace3,5\rbrace \\ A^(\prime)\cap C^(\prime)=\lbrace\rbrace=\Phi \end{gathered}`

No common elements between A' and C'

c. (A intersects B)' means all elements in U except the common elements between A and B

`\begin{gathered} A\cap B=\lbrace5\rbrace \\ \\ (A\cap B)^(\prime)=\lbrace1,2,3,4,6\rbrace \end{gathered}`