Question

show s is a valid conclusion p⇒q,p⇒r,~(qnr),svp​

Answer 1

Answer:

Therefore, we will be home by sunset.

To determine if this argument is valid, we should begin by translating it into logic. Let p denote "It is sunny this afternoon", q denote "It is colder than yesterday", r denote "We will go swimming", s denote "We will take a canoe trip" and t denote "We will be home by sunset." The premises are therefore ¬p∧q, r→p, ¬r→s, s→t and the conclusion is t. Apply the following rules of inference.

1.2.3.4.5.6.7.8.¬p∧qr→p¬r→ss→t¬p¬rst∴tSimplification (1)Modus Tollens (2,5)Modus Ponens (3,6)Modus Ponens (4,7)