Math Logic Drawing Conclusions and Laws

Question 1

Law Of Modus Tollens

Answer 1

P→q
-q
——
-P is true
In a true conditional, when a conclusion is false, the hypothesis must also be false

Question 2

Law Of Detachment

Answer 2

P→q
P
——
Q is true

True hypothesis needs to have true conclusion to be true

Question 3

Conjunctive simplification

Answer 3

p^q
p is true q is true
Both have to be true in a conjunction

Question 4

Law of contrapositive

Answer 4

P→Q
-Q→-P is true

If you get a sentence that is a true statement, the contrapositive of the statement always has a valid conclusion.

Question 5

Disjunctive Inference

Answer 5

Pvq
-P
——
Q is true
When a disjunction is true and one of them is false, the other one must be true

Question 6

Chain Law

Answer 6

P→Q
Q→R
——-
P→R is true

Question 7

DeMorgan’s Law #1

Answer 7

-(P^Q)
-Pv-Q is true

Question 8

DeMorgan’s Law #2

Answer 8

-(PvQ)
-P^-Q is true