**Rules of inference (8)**

Modus Ponens

MP p > q / p // q

Modus Tollens

MT p > q / ~q // ~p

Hypothetical syllogism

HS p > q / q > r // p > r

.

Disjunctive syllogism

DS p v q / ~p // q

Simplification

SM p . q // p

Conjunction

CN p / q // p. q

Addition

AD p // p v q

Constructive Dilemma

CD (p > q) . (r > s) / p v r // q v s

**Rules of Equivalence/ Replacement (10) **

Double Negation

DN p :: ~~p

Commutation

CM (p . q) :: (q . p) (p v q) :: (q v p)

Association

AS ((p . q) . r) :: (p . ( q . r)) ((p v q) v r) :: (p v (q v r))

DeMorgan’s Rule

DM ~(p v q) :: (~p . ~q) ~(p .q) :: (~p v ~q)

Distribution

DIST (p v (q . r)) :: ((p v q) . (p v r)) (p . (q v r)) :: ((p . q) v (p . r))

Transposition

TRAN (p > q) :: (~q > ~p)

Implication

IMP (p v q) :: (~p > q)

Equivalence

EQ (p ≡ q) :: ((p > q) . (q > p)) (p ≡ q) :: ((p . q) v (~p . ~q))

Exportation

EXP (p > (q > r)) :: ((p . q) > r)

Tautology

TAUT (p v p) :: p (p . p) :: p

Modus ponens is the elimination rule for the logical connective in formal logic (forming conditional statements).

This is function application on more broad types in type theory.

Even in Hilbert-style logic, where there are essentially no rules of inference (apart from the numerous axioms), a rule of modus ponens is generally present. (In particular, in Hilbert’s version of the propositional calculus, modus ponens is the only non-axiom rule of inference.)

Thanks for sharing this. I really enjoyed reading it. It is very good. This is interesting as well as very engaging. I couldn’t stop until I finished it.

The description of slope unblocked.

Welcome to Slope! Easy on start, but extra challenging and fun during the run!

Slope unblocked Game, you take control of a ball rolling down a steep slope. As you steer from side to side, your game plan is to avoid colliding into obstacles, keep your ball straight onto the falling slopes, speed boosting along the way and have tons of adrenaline rushed fun as you strive attain your record! The further you get, the faster you go! Easy on sight, extra challenging and fun during the run! For added challenge, the course is randomized each slopes platforms, speed boosters, obstacles and tunnels, every time you play, forcing you to constantly stay on high alert if you want to succeed.

Mobile games have made our routine life very entertaining and decreased our mental problems as well. I have just got assignment writing service and completed my essays. These games have probably brought revolution in our lives which is a very good sign at all.