Hello

LetA, B and C be 3 sets. Prove that:

if x belongs to (A-B)-C then x belongs to A-C using:

a)direct proof.

b)proof by contraposition

thank you

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- Dec 18th 2008, 06:53 AMqwerty321set proof
Hello

LetA, B and C be 3 sets. Prove that:

if x belongs to (A-B)-C then x belongs to A-C using:

a)direct proof.

b)proof by contraposition

thank you

- Dec 18th 2008, 07:22 AMIsomorphism
a) $\displaystyle x \in A \cap B^c \cap C^c \Rightarrow x \in A, x \notin B, x \notin C \Rightarrow x \in A, x \notin C \Rightarrow x \in A$\$\displaystyle C$

b) $\displaystyle x \notin A$\$\displaystyle C \Rightarrow x \notin A, x \in C \Rightarrow x \in A^c \cup C \Rightarrow x \in A^c \cup B \cup C \Rightarrow x \in (A \cap B^c \cap C^c)^c \Rightarrow x \notin (A$\$\displaystyle B)$\$\displaystyle C$

Thus $\displaystyle x \notin A$\$\displaystyle C\Rightarrow x \notin (A$\$\displaystyle B)$\$\displaystyle C$

Which is proof of the contrapositive. - Dec 18th 2008, 07:45 AMqwerty321
when you pu the little c above A or B, what do u mean?

and for the contrapositivity how did u pass from x belongs to A^cUC to A^cUBUC?

thank you - Dec 18th 2008, 07:50 AMIsomorphism