- #1

Shackleford

- 1,656

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I'm taking Abstract Algebra right now, and we just briefly covered Logic and Truth Tables. This is my first time in school to learn such things.

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110712_195458.jpg

37. I understand.

39. I understand.

41. I don't understand the last column. Is the implication (p ∧ q) ⇒ p true because (p ∧ q) gives you no information on whether p is true? Why?

43. For p ⇒ q, I understand the first two column entries (T,F), is the implication because p being False gives no information on whether p ⇒ q is True? Again, for the last column, is

(p ∧ (p ⇒ q)) True because it being False gives you no new information on q?

If my reasoning is correct, then I can see the following logical consistencies here. Also, I notice for the implications ⇒, there is an additional column asking for its truth value. But, there is no such thing for the iff ⇔ statements. Why?

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110712_195458.jpg

37. I understand.

39. I understand.

41. I don't understand the last column. Is the implication (p ∧ q) ⇒ p true because (p ∧ q) gives you no information on whether p is true? Why?

43. For p ⇒ q, I understand the first two column entries (T,F), is the implication because p being False gives no information on whether p ⇒ q is True? Again, for the last column, is

(p ∧ (p ⇒ q)) True because it being False gives you no new information on q?

If my reasoning is correct, then I can see the following logical consistencies here. Also, I notice for the implications ⇒, there is an additional column asking for its truth value. But, there is no such thing for the iff ⇔ statements. Why?

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