(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

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# Homework Help: Logical Proof

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