Conditional Statements
The conditional statement in logic notation
What is
p -> q
The converse of a conditional statement in logic notation
What is
q -> p
The inverse of a conditional statement in logic notation
What is
~ p -> ~ q
The contrapositive of a conditional statement in logic notation
What is
~ q -> ~p
P: "It is raining"
~P: ...
What is ~P: "It is not raining"
p and q stands for?
p: hypothesis
q: conclusion
How do you create the converse of a conditional statement
What is "Switch the hypothesis and conclusion."?
How do you create the inverse of a conditional statement
What is "Negate both the hyopthesis and conclusion"?
How do you create the contrapositive of a conditional statement
What is "Negate both the hypothesis and conclusion and switch them."?
P ^ Q
What is P ^ Q: " It is raining and I will stay home."
"If a figure is a square, then it is a rectangle." What is the hypothesis of the conditional statement?
What is "A figure is a square."
The converse of "If a number is divisible by 2, then it is even?"
What is "If a number is even, then it is divisible by 2."
What is "If a figure is not a square, then it is not a rectangle."?
Contrapositive of the statement: "If a figure is a square, then it is a rectangle."
What is "If a figure is not a rectangle, then it is not a square."
Given
P: "The figure is a square."
Q: "The figure is a rectangle."
R: "The figure has congruent diagonals."
(P^Q)^R
What is "The figure is a square or a rectangle, and it has congruent diagonals."
The hypothesis of the statement "An angle measures 90 degrees if it is a right angle"
What is "An angle is a right angle"
True or False? The converse and the inverse always have the same truth value as the conditional.(They are logically equivalent to the conditional)
Ex. Conditional: If it rains, the ground is wet.
Converse: If the ground is wet, it rains.
Inverse: If it does not rain, the ground is not wet.
What is FALSE
True or False? The inverse and the converse always have the same truth value. (They are logically equivalent to each other)
Ex.
Inverse: If a person is not a professional soccer player, then they do not play in the NFL.
Converse: If a person plays in the NFL, then they are a professional soccer player.
What is TRUE
True or False? A conditional statement and its contrapositive always have the same truth value.
What is TRUE
Given
P: "The figure is a square."
Q: "The figure is a rectangle."
R: "The figure has congruent diagonals."
Either the figure is not a square or the figure is a rectangle, and the figure does not have congruent diagonals.
What is (~P V Q) ^ ~R
Change "A student is prepared for a test if they study regularly" into a conditional statement.
What is "If a student studies regularly, then they are prepared for a test."
Converse of the following statement "A figure has four congruent sides if it is a rhombus."
What is "If a figure has four congruent sides, then it is a rhombus."?
Inverse of the following statement: "A driver receives a safe driving score if they stop at a red light."
What is "If a driver does not stop at a red light, then they do not receive a safe driving score."?
Contrapositive of the statement: "A person graduates if they complete the required credits."
Given
P: "The figure is a square."
Q: "The figure is a rectangle."
R: "The diagonals are congruent."
S: "The diagonals are perpendicular."
The figure is a rectangle or not a square, and the diagonals are congruent or perpendicular.
What is (P V ~Q) ^ (R V S)