Question

Which of the following are true about x? Check all that apply. X ∉ A x ∈ B x ∉ C x ∈ A ⋃ B x ∈ A ⋃ C x ∈ A ⋂ B.

Answer 1

You can use those given Venn diagram to deduce where does x lies.

The options that are true are:

Option B: x ∈ B

Option C: x ∉ C

Option D: x ∈ A ⋃ B

Option E: x ∈ A ⋃ C

Option F: x ∈ A ⋂ B

When do we say that x belongs to some set S?

If x resides inside the set S, then we say that x belongs to set S and we write this fact symbolically as:

$x \in S$

If x doesn't belong inside the set S, then we write it as:

$x \notin S$

Example, if S = {1,2,3}, then let x = 3, then we say that 3 ∈ S

What are union and intersection of two sets A and B?

For given Venn diagram, we can see that x lies inside A and B and the area where both A and B lies (A intersection B, written as A ⋂ B)(intersection of A and B is common area of both A and B).

Union of A and B is the whole area where A and B lies. It is denoted by

A ⋃ B

Since in this whole area,  x is present, thus we say x ∈ A ⋃ B

Since x lies in the union of A and C too( the area where A and B wholly lie), thus we write x ∈ A ⋃ C

Thus, we have:

$x \in A\\ x \in B\\ x \in A \cap B\\ x \in A \cup B\\ x \in A \cup C$

since x doesn't belongs to C, thus we can write $x \notin C$

Thus, these options are correct:

Option B: x ∈ B

Option C: x ∉ C

Option D: x ∈ A ⋃ B

Option E: x ∈ A ⋃ C

Option F: x ∈ A ⋂ B

Learn more about sets using Venn diagram here:

https://brainly.com/question/26090333