D. Directions. Translate the following 5 sentences into symbolic notation using

Question

D. Directions. Translate the following 5 sentences into symbolic notation using the translation dictionary here: A = the key is aluminum; B = the key is brass; C = the key is clean; F = the key will fit the lock;

1. The key being clean is not a sufficient condition for it to fit the lock.

2. The key won’t fit if it isn’t clean.

3. Neither is the key brass nor is it aluminum.

4. The key isn’t brass, but if it were, then it would fit the lock.

5. The key isn’t clean; however, it will fit and it’s made of brass.

Explanation / Answer

A = the key is aluminum; B = the key is brass; C = the key is clean; F = the key will fit the lock;

1. The key being clean is not a sufficient condition for it to fit the lock.

~ (C -> F)

2. The key won’t fit if it isn’t clean.

~C -> ~F

3. Neither is the key brass nor is it aluminum.

~B & ~A

4. The key isn’t brass, but if it were, then it would fit the lock.

~B ^ (B -> F)

5. The key isn’t clean; however, it will fit and it’s made of brass.

~C ^ F ^ B

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