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Level 149

Conditional Statements


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conditional statement
a logical statement containing two parts: hypothesis and conclusion.
hypothesis
an educated guess
Negation of a statement
P is "not P" written as ̴ p
converse statement
if q, then p
Inverse statement
if ~p, then ~q
Contra-positive statement
̴ Q --> ̴ P
Bi-conditional statement
P if and only Q
If-then form
the "if" part contains the hypothesis and the "then" part contains the conclusion.
Conclusion
Tells if your hypothesis was correct; supported or not supported
Converse
(noun) A statement that switches the hypothesis and conclusion
Negation
Adding "not" or removing it
Inverse
reversed (turned backward) in order or nature or effect
Contrapositive
when the hypothesis and the conclusion of a converse of a conditional statement are negated
equivalent statements
have the same truth value
Perpendicular lines
lines in a plane that intersect to form 4 right angles
Line Perpendicular to a Plane
a line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it
Biconditional Statement
p if and only if q
Law of Detachment
is p-->q is true, then p is true, and q is true
Law of Syllogism
if p-->q and q-->r are true, then p-->r is true
Logical Argument
an argument based on deductive reasoning, which uses facts, definitions, and accepted properties in a logical order
- conditional statements
Types of Statements used in logical argument
Conditional statements
statements written using if & then
The hypothesis (the "if" statement)
Two parts of the conditional statements
If hypothesis then conclusion
how to write a conditional statement
Inverse
a + (-a) = 0 = (-a) + a OR a * 1/a = 1 = 1/a * a; a cant be 0
conditional
an if-then statement
Biconditional
Conditional statement where both the converse and inverse are true and uses the phrase "if and only if"