In each of the following, determine whether the statement is true or f

1.	In each of the following, determine whether the statement 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) If A⊂B and B∈C then A∈C (iii) If 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 statement 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 $x \in B$ (ii) If $A \subset B$ and $B \in C$ then $A \in C$ (iii) If $A \subset B$ and $B \subset C$ then $A \subset C$ (iv) If $A \subset̸ B$ and $B \subset̸ C$ then $A \subset̸ C$ (v) If $x \in A$ and $A \subset̸ B$ then $x \in B$ (vi) If $A \subset B$ and $x \notin B$ then $x \notin A .$

In each of the following, determine whether the statement 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) If A⊂B and B∈C then A∈C (iii) If 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 statement 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 $x \in B$

(ii) If $A \subset B$ and $B \in C$ then $A \in C$

(iii) If $A \subset B$ and $B \subset C$ then $A \subset C$

(iv) If $A \subset̸ B$ and $B \subset̸ C$ then $A \subset̸ C$

(v) If $x \in A$ and $A \subset̸ B$ then $x \in B$

(vi) If $A \subset B$ and $x \notin B$ then $x \notin A .$