Logical Arguments | Geometry H TGHS G9 25-26

p

Hypothesis

q

Conclusion

~ or ¬

Negation

The opposite of the statement.

p → q

Conditional

If p, then q.

q → p

Converse

If q, then p.

~p → ~q

Inverse

If not p, then not q.

~q → ~p

Contrapositive

If not q, then not p.

p ∧ q

Conjunction

p and q.

p ∨ q

Disjunction

p or q.

p ↔ q

Biconditional

p if and only if q.

If p → q is true

and p is true,

then q is true.

Law of Detachment

If the hypothesis of a true confirmational is true, then the conclusion is true.

If p → q is true

and q → r is true,

then p → r is true.

Law of Syllogism

Allows you to state a conclusion from two true conditional statements.

p → q

q → r

p → r