Logical inference

Question 1

Converse of p -> q

Answer 1

q->p

Question 2

Inverse of p->q

Answer 2

¬p->¬q

Question 3

Contrapositive of p->q

Answer 3

¬q->¬p

Question 4

What is and does biconditional of p->q mean

Answer 4

means “p if and onl yof q” the biocondition is p<->q which evaluates to true if p and q are same truth value

Question 5

What is modus ponenus

Answer 5

1. p
2. p->q
   (c) q

Question 6

Modus Tollens

Answer 6

1.p->q
2.¬q
(c) ¬p

Question 7

Addition

Answer 7

1.p
(c) pvq

Question 8

Simplification

Answer 8

MULTIPLE WAYS OF DOING THIS

Question 9

conjunction

Answer 9

line x ∧ line y

Question 10

Resolution

Answer 10

1.p v q
2.¬p v r
(c) q v r

Question 11

Disjunctive Syllogism

Answer 11

1. pvq
2. ¬p
   (c) q

Question 12

Hypothetical Syllogism

Answer 12

1. p -> q
2. q -> r
   (c) p -> r

Question 13

logical equivalence of pvq -> r is what

Answer 13

1 and 2 are equal
1. (pvq) -> r
2. (p->r ) ∧ (q->r)

Question 14

Demorgans Law

Answer 14

1. ¬(p∧q) == ¬p v ¬q
2. ¬(pvq) == ¬p ∧ ¬q

Question 15

Associotivity means what?

Answer 15

for p v q v r brackets can be anywhere and still mean the same i.e
(p v q) v r == p v (q v r)

Question 16

Distributivity means what

Answer 16

p ∧ (q v r ) == (p∧q) v (p∧r)

Question 17

Commutative means what

Answer 17

any order
pvq == q v p
p∧ q == q∧ p

Question 18

Absorbtion means what

Answer 18

pv (p∧q) == p
p ∧ (pvq) == p

Question 19

How to transform a conditional to a dysfunction

Answer 19

p -> q == ¬pvq