Symbols
What is the symbol for negate?
~
What is a conditional statement?
A statement that can be written in "if...then" form.
Hypothesis: Mrs. Millar buys a new pet
Conclusion: She will get a penguin
What is the Law of Syllogism?
If a first event implies a second and the second implies a third, then the first event implies the third event.
1. If p-->q
2. If q -->r
3. Then p -->r
What is the 1st reason in a proof?
Given
What is the symbol for "if...then"?
-->
Describe the hypothesis and conclusion of a conditional statement.
Hypothesis: The part of a conditional statement that follows "if", symbol: p
Conclusion: The part of a conditional statement that follows "then", symbol q
What is the contrapositive to the following statement: If I study, then I will get an A on the test ?
I will not get an A on the test, if I do not study.
What is the Law of Contrapositive?
The original statement is true, if and only if the contrapositive is true.
Conditional statement is logically equivalent to its contrapositive.
Describe the transitive property.
Similar to the law of syllogism
If a=b and b=c, then a=c.
When do you use this symbol, <-->?
Biconditionals
If and only if
What is a converse of a conditional statement?
Statement formed when the hypothesis & conclusion are switched
q --> p
What is the logically equivalent statement to the conditional statement: If I am at Virginia Tech, then I am in Virginia ?
If I am not in Virginia, then I am not at Virginia Tech.
What is the Law of Detachment?
If p leads to q and p is true, then q must be true.
When proving x=-10 with the given equation:
2(4-x)-5x=78, what is the 2nd reason?
Distributive Property
Write the inverse of a conditional statement in symbols.
~p --> ~q
What is the inverse of a conditional statement?
Statement formed by negating both the hypothesis and conclusion.
~p --> ~q
What is the true biconditional statement to the conditional: If a triangle is equilateral, then the triangle has all congruent sides ?
A triangle is equilateral if and only if the triangle has all congruent sides.
Given the following statements, what is a valid conclusion?
If Keaton wears a blue shirt, then we will take a test.
If we take a test, then everyone will pass the test.
If Keaton wears a blue shirt, everyone will pass the test.
If the statement in a proof states, "(x/3)+5=20", what property is the reason when solving for the variable?
Subtraction Property of Equality
Write the contrapositive for a conditional statement in symbols.
~q --> ~p
What is the contrapositive of a conditional statement?
The statement formed by writing the converse of the inverse.
Switching the hypothesis and conclusion and negating both
~q --> ~p
Statement 1: If I did all of my work, then I will do well on my test.
Statement 2: If I did not do all of my work, then I will not do well on my test.
Statement 2 is the inverse of statement 1.
Given the following statements, what is the logical conclusion?
If a shape is a parallelogram, then opposite angles are congruent. A rhombus is a parallelogram
A rhombus has opposite angles that are congruent.
Which algebraic property states if a=b, then b=a?
Symmetric Property of Equality