Postulates and Conditionals

What is a conditional statement

What is the formula of and if then statement

p(arrow)q

What is the definition of a converse statement?

Writing the conditional by swapping the hypothesis with the conclusion

What is the definition of a inverse statement?

Write the conditional after negating both the hypothesis and conclusion

What is the definition of a Contrapositive statement?

The negation of the converse. You first swap the Hypothesis and conclusion then make both parts negative.

What is the definition of a counterexample?

An example of something that disproves a statement

What is a conjecture

An unproven statement based on observation

What is inductive reasoning

A statement made from observations of patterns and assumptions

What is deductive reasoning

An argument that uses logic, definitions, facts, accepted properties and more. Is always true

What is the two point postulate about

Through any two points there exists exactly one line

What is the line-point postulate about

A line contains at least 2 points

What is the line intersection postulate about

If two lines intersect, they have exactly one point in common

What is the three point postulate about

Through any three collinear points there exists exactly one plane

What is the plane-point postulate about

A plane contains at least 3 noncollinear points

What is the plane-line postulate about

If two points lie on a plane then the line containing them lies in the plane

What is the plane intersection postulate about

If two planes intersect then their intersection is a line

What is the converse of the two point postulate

The line point postulate

What is the converse of the plane-point postulate

The three point postulate

What is a negation

The opposite of the original statement. (ex. the ball is red (og) the ball is not red (changed)

WHat is the symbol of a negation

~p

What is the symbol of a converse

q→p

What is the Law of detachment about

If the hypothesis of a true conditional statement is true then the conclusion is also true

What is the Law of Syllogism about

If p→q and q→r are both correct then p→r is correct

What is the symbol of an inverse statement

~p → ~q

What s the symbol of a contrapositive statement

∼𝑞→∼𝑝

What is the symbol of a conditional statement

p→q

What is the word formula of a conditional statement

If (hypothesis) then (conclusion).

p representing the hypothesis and q representing the conclusion

What is the definition of a postulate

A statement accepted to be true without proof