Inference Rule (Descrete Maths Question)

Question

If Lowell is Studyiing for the ministry, then he is required to take theology and greek.

Lowell is not reuqired to take greek.

Hence, Lowell is not studying for the ministry.

(is this valid/tautology or not?)

Answer 1

Convert the given logical argument into logical variables
Let P : Lowell is studying for the ministry
Let Q : Lowell is required to take theology and Greek.
If P, then Q (P→Q)
Not Q (¬Q)

Hence, not P(¬P).

 

Sol:
  P → Q    | make premises true
  ¬Q → T   |                  T
  _________|_________F

  ¬P       | make it False
  ↓        |       False
  T

P = T

¬P = F             : we could not make premises True,
                     So it's a valid argument

Answer 2

its a valid argument p implies q and r and q is false means q and r false hence t -> f = f  and the argument is lowell is not studing for the ministry is true because p-> ~q  = f