Inference Rules-Week 7

Up to today, we have learned some rules of inference to allow us to reach conclusions about certain situations. Here are some of them:

Conjunction Elimination: if we know A^B, we can conclude A and B are both True.

Existential Elimination: if we know that there exist a belongs to X, P(a), then we can certainly pick an element with that property. Pick a' belongs to X, then p(a').

Disjunction Elimination: if we know that A V B, and we know that not(A), we can conclude that B must be True.

Implication Elimination: if we know A implies B, and we also know that A is True, we can conclude that B is also True. On the other hand, if we know not(B), we must conclude that not(A) must be True.

Universal Elimination: if we know that for all x belongs to X, P(x), then if we choose any a belongs to X, we can conclude that P(a) must be True.

Implication introduction:if we assume A and then B follows, then we can conclude that A implies B

Universal Introduction: if we assume that a is generic element of D, and we derive P(a), then we can conclude that for all a belongs to D, P(a).

Existential Introduction:if we can show that x belongs to X, P(x), then we can conclude that there exist x belongs to X, such that P(x).

Conjunction introduction:if we know that A and we know B, then we can conclude A^B

Disjunction introduction: If we know A, we can immediately conclude that A v B