Question

. Determine whether the conclusion C fallows logically from the premises H1&H2

i H1:p->q H2:p C:q

ii H1:p->q H2:~p C:q

Answer 1

Answer:

Step-by-step explanation:

(i) H1: p → q H2: p

⇒ H1 ∩ H2

⇒ (p → q) ∩ p

⇒ ((negation p) ∪ q) ∩ q                        ∵p → q = (negation p) ∪ q

⇒ ((negation p) ∩ p) ∪ (q ∩ p)

⇒ q ∩ p                                                   ∵ ((negation p) ∩ p) is always False

(ii) H1: p → q H2: negation p

⇒ H1 ∩ H2

⇒ (p → q) ∩ negation p                              ∵p → q = (negation p) ∪ q

⇒ ((negation p) ∪ q) ∩ negation p

⇒ (negation p ∩ negation p) ∪ (q ∩ negation p)

⇒ True or (q ∩ negation p)

Answer 2

Answer:

Step-by-step explanation:

Applications of Logic: This is a fluid area of study. Model Theory is being used in increasingly complex ways to various areas of mathematics, while Proof Theory, Complexity Theory, and the study of Reasoning under Uncertainty are being applied to computer science, artificial intelligence, and IT.

Mathematical logic applications It was created to codify accurate information and sound logic. Leibniz, Boole, and Frege, who founded it, intended to utilise it for common sense facts and reasoning; nevertheless, they were unaware that the imprecision of common sense notions was frequently a required feature rather than always a flaw.

Definition of Proposition (Statement): A proposition is a declarative statement that can be true or untrue, but not both.

H2: p I H1: p q

⇒ H1 ∩ H2

⇒ (p → q) ∩ p

Negation p, positive q, and negative p, positive q, and positive p. q = (p-negative)q

(Q p) ((negation p) p)

Negation p is always false according to the formula q p ((negation p) p)

H1: p q H2: negation p (ii)

⇒ H1 ∩ H2

(p q) = (negation p) q

Negation p ((negation p)) q Negation p

Negation p negates negation p, and vice versa.

Either true or (q p negation)

For more details on Essay Writing, https://brainly.in/question/28301617

#SPJ1