Part 4: Choose the option for the correct answer. You do not have to name the ru
ID: 2075900 • Letter: P
Question
Part 4: Choose the option for the correct answer. You do not have to name the rule. (3 points, each, 15 total)
1. _______ If you have P -> Q, and you want to infer Q, what other information do you need?
a. P
b. ~ P
2. ________If you have P -> Q and you want to infer P -> R, what other information do you need?
a. R -> Q
b. Q -> R
3. ________If you have P -> Q, and you want to infer ~ P, what other information do you need?
a. Q
b. ~ Q
4. ________If you have P and you want to infer P v Q, what other information do you need?
a. Nothing else is needed.
b. Q
5. _________ If you have P and you want to infer P & Q, what other information do you need?
a. Nothing else is needed.
b. Q
Explanation / Answer
1) If we have P Q, and we want to infer Q
Implication P Q can be represented as:
P Q ~ P V Q
So, if we know P, then
~ P V Q V P Q
we can infer Q.
ans: a
2) If we have P Q, and we want to infer P R
we should know Q R, as using Hypothetical syllogism which states that
if we have:
i) P Q
ii) Q R
then P R
ans: b
3) If we have P Q, and we want to infer ~ P
Implication P Q can be represented as:
P Q ~ P V Q
So, if we know ~ Q, then
~ P V Q V ~ Q ~ P
we can infer ~ P
ans: b
4) If we have P and we want to infer P V Q
then we should know Q only as then we can infer P V Q
if nothing is known then for the following two cases if:
i) P is True then P V Q will be True always. Here P V Q doesn't depend on Q. But when
ii) P is False then P V Q will be True if Q is True and False if Q is False . Here P V Q depend on Q.
So, we require Q to infer P V Q
ans. b
4) If we have P and we want to infer P Q
then we should know Q only as then we can infer P Q
if nothing is known then for the following two cases if:
i) P is False then P Q will be False always. Here P V Q doesn't depend on Q. But when
ii) P is True then P Q will be True if Q is True and False if Q is False . Here P Q depend on Q.
So, we require Q to infer P Q
ans. b