- #1

ajsingh

- 18

- 0

## Homework Statement

To prove [tex]A \subseteq C and B \subseteq C[/tex] implies [tex](A \cup B)\subseteq C[/tex]

**2. The attempt at a solution**

I just wanted to know if my reasoning seems logical. Here is my attempt:

Assume [tex]A \subseteq C and B \subseteq C ... (1) [/tex]

Assume [tex]\forall x [ x\in A] and \forall x [x \in B] ... (2) [/tex]

Hence, from definition of [tex]\bigcup \forall x [x \in A \cup B ] ... (3)[/tex]

From (1) and defination of [tex]\subseteq, \forall x [ x \in A \Rightarrow x \in C and x \in B \Rightarrow x \in C ] ..... (4)[/tex]

Hence, [tex]\forall x [x \in A \cup B \Rightarrow x \in C] ..... (5)[/tex]

[tex]\Rightarrow (A \cup B) \subseteq C

[/tex]

Does that seem to flow logically?

Thanks