Recall, from the notes, we proved that for any set B, we have B. We proved...

 

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Recall, from the notes, we proved that for any set B, we have B. We proved this via contradiction. However, now I want you to reprove it, but not by any kind of indirect proof. Here, whip out the appropriate truth table and see that 0) CB is immediately true! [Note: this is really quick, and to me feels more like a simple observation than a full-blown proof.] Use a direct proof to prove the following statement, where A, B, C are sets: If ACB, then AnCC BNC and AUC C BUC. [Note: don't be thrown off by the desired conclusion, which is two separate statements. that need proof. Just handle each separately within the same proof.] Recall, from the notes, we proved that for any set B, we have B. We proved this via contradiction. However, now I want you to reprove it, but not by any kind of indirect proof. Here, whip out the appropriate truth table and see that 0) CB is immediately true! [Note: this is really quick, and to me feels more like a simple observation than a full-blown proof.] Use a direct proof to prove the following statement, where A, B, C are sets: If ACB, then AnCC BNC and AUC C BUC. [Note: don't be thrown off by the desired conclusion, which is two separate statements. that need proof. Just handle each separately within the same proof.]

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To prove the statement If AC B then ANCCBOC and AUC C BUC using a direct proof well show that both s... View the full answer