Conditional Statements
It's the hypothesis in the following conditional statement: "If it snows, then we don't have school."
What is "It snows?"
This symbol denotes the hypothesis of a conditional statement.
What is, "p"?
This is the law of logic used in the following logical argument:
"If it is Wednesday, then I will get pizza.
I got pizza.
Therefore, it is Wednesday."
What is the Law of Detachment?
This conclusion can be drawn from the following logical argument:
"If there is no water, then the cows will be thirsty.
There is no water."
What is, "Therefore, the cows will be thirsty."
This symbol denotes when a statement is negated.
What is "~"?
It's the conclusion of the following conditional statement: "If we have tickets, then we can go to the show."
What is "we can go to the show?"
Let p refer to "it is raining"
Let q refer to "the sun is not out"
This is the symbolic form of the following statement:
"If it is not raining, then the sun is out."
What is, "~p → ~q"?
This is the law of logic used in the following logical argument:
"If the sun is shining, then I will go to the park.
I am not going to the park.
Therefore, the sun is not shining."
What is the Law of Contrapositive?
This conclusion can be drawn from the following logical argument:
"If there are clouds in the sky, then it is not sunny.
It is sunny."
What is, "Therefore, there are not clouds in the sky."
This book is an excellent example of how the Law of Syllogism works.
What is "If You Give a Mouse a Cookie?"
This is the inverse of the following conditional statement: "If the cats are sleeping, then they are are not hungry."
What is, "If the cats are not sleeping, then they are hungry?"
This is the symbol that denotes the phrase "if and only if."
What is, "↔"?
These laws have given information in the form of:
p → q
q → r
What are the Law of Syllogism and the Law of Syllogism with Contrapositive?
This conclusion can be drawn from the following logical argument (using Syllogism):
"If the stars are shining bright, then we can see them.
If we can see the stars, then it is nighttime."
What is, "Therefore, if the stars are shining bright, then it is nighttime."
This is the distance between the points (3,2) and (-5,1).
What is √65
This is the biconditional of the following conditional statement: "If we go running, then it is sunny outside."
What is, "We go running if and only if it is sunny outside?"
Let p refer to "I study"
Let q refer to "I do my homework"
Let t refer to "I will get a good grade"
This is the symbolic form of the following statement:
"If I study and do my homework, then I will get a good grade."
What is, "p ∧ q → t"?
This law is used in the following logical argument:
"If you drive 51 miles southeast, then you will be in Williamsburg.
If you are in Williamsburg, then you are near Busch Gardens.
Therefore, if you are not near Busch Gardens, then you did not drive 51 miles southeast."
What is the Law of Syllogism with Contrapositive?
This conclusion can be drawn from the following logical argument:
"If they don't go to the dance, then they are not having fun.
They are having fun."
What is, "Therefore, they went to the dance."
Is the following logical argument valid or invalid?
"If we are going to New York, then we ride the train.
If we ride the train, then we need to buy a ticket.
Therefore, if we do not buy a ticket, then we are not going to New York."
Valid
This is the contrapositive of the following conditional statement: "If the teachers assigned homework, then the students are not happy."
What is, "If the students are happy, then the teachers did not assign homework."
Let s refer to "it is summer"
Let w refer to "it is the weekend"
Let r refer to "we have school
This is the symbolic form of the following statement:
"If it is summer or it is the weekend, then we do not have school."
What is, "s ⋁ w → ~r?"
This law is used in the following logical argument:
"If Aang travels with Katara and they see the cabbage merchant, then there is trouble.
Aang is traveling with Katara and they see the cabbage merchant.
Therefore, there is trouble."
What is the Law of Detachment?
This conclusion can be drawn from the following logical argument (using Syllogism with the Law of Contrapositive):
"If the students are wearing white, then they are freshmen.
If they are freshmen, then they are participating in spirit week."
Is the following logical argument valid or invalid?
"If we sing and dance, then we are celebrating.
We are celebrating.
Therefore, we sing and dance."
Invalid