Hi. I am new to formal proofs. Is the following a legitimate method for proving this assertion by contradiction.(adsbygoogle = window.adsbygoogle || []).push({});

Show [tex]A\cap B = \{\} \Leftrightarrow A \subseteq B^c[/tex]

If [tex]A\cap B \neq \{\} [/tex] then [tex]\exists \ x \ ST \ x \in A \ AND \ x \in B [/tex]

Since [tex]x \in A \ \ \ A \subseteq B^c \Rightarrow x \in B^c[/tex]

[tex]\Rightarrow x \in U \ AND \ x \notin B [/tex]

This is a contradiction and thus no such x exists and therefore

[tex]A\cap B = \{\} \Leftarrow A \subseteq B^c[/tex]

is this half the proof?

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# Does this constitute a proof

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