In each of the following, determine whether the statements is true or false. If it is true, prove it. If it is false, give an example.(i) If x∈A and A∈B, then x∈B(ii) A⊂B and B∈C, then A∈C(iii) A⊂B and B⊂C, then A⊂C(iv) If A⊄B and B⊄C, then A⊄C(v) If x∈A and A⊄B, then x∈B(vi) If A⊂B and x∉B, then x∉A

In each of the following, determine whether the statements is true or

1.	In each of the following, determine whether the statements is true or false. If it is true, prove it. If it is false, give an example.(i) If x∈A and A∈B, then x∈B(ii) A⊂B and B∈C, then A∈C(iii) A⊂B and B⊂C, then A⊂C(iv) If A⊄B and B⊄C, then A⊄C(v) If x∈A and A⊄B, then x∈B(vi) If A⊂B and x∉B, then x∉A
Answer» In each of the following, determine whether the statements is true or false. If it is true, prove it. If it is false, give an example. $(i)$ If $x \in A$ and $A \in B$ , then $x \in B$ $(i i)$ $A \subset B$ and $B \in C$ , then $A \in C$ $(i i i)$ $A \subset B$ and $B \subset C$ , then $A \subset C$ $(i v)$ If $A \subset̸ B$ and $B \subset̸ C$ , then $A \subset̸ C$ $(v)$ If $x \in A$ and $A \subset̸ B$ , then $x \in B$ $(v i)$ If $A \subset B$ and $x \notin B$ , then $x \notin A$