Q:

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

Accepted Solution

A:
You can use those given Venn diagram to deduce where does x lies.The options that are true are:Option B: x ∈ BOption C: x ∉ COption D: x ∈ A ⋃ B Option E: x ∈ A ⋃ COption F: x ∈ A ⋂ BWhen 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:[tex]x \in S[/tex]If x doesn't belong inside the set S, then we write it as:[tex]x \notin S[/tex]Example, if S = {1,2,3}, then let x = 3, then we say that 3 ∈ SWhat 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 ⋃ BSince in this whole area,  x is present, thus we say x ∈ A ⋃ BSince x lies in the union of A and C too( the area where A and B wholly lie), thus we write x ∈ A ⋃ CThus, we have:[tex]x \in A\\ x \in B\\ x \in A \cap B\\ x \in A \cup B\\ x \in A \cup C[/tex]since x doesn't belongs to C, thus we can write [tex]x \notin C[/tex]Thus, these options are correct:Option B: x ∈ BOption C: x ∉ COption D: x ∈ A ⋃ BOption E: x ∈ A ⋃ COption F: x ∈ A ⋂ BLearn more about sets using Venn diagram here: