Inverse Statement
If the weather is nice, then I will wash the car.
If the weather is not nice, then I won't wash the car
If phones and video games weren't invented, then we would all be more sociable.
If we would all be more sociable, then phones and video games weren't invented
If you skip leg day, then you'll have chicken legs.
If you don't have chicken legs, then you didn't skipped leg day.
What is the contrapositive of the following statement?
If Sally is 6 feet tall, then she plays basketball.
If Sally does not play basketball, then she is not 6 feet tall
p= You are fast
q= You can beat an ostrich
p - ~q
You are fast, and you cannot beat an ostrich.
Mary's mum has four children. The first child is called April. The second is May. The third is June. What is the name of the fourth child?
Mary
P: "It is raining."
Q: "The ground is wet."
R: "I will carry an umbrella."
P ∧ Q
It is raining AND the ground is wet.
If I love milk chocolate, then I hate dark chocolate.
If I don't love milk chocolate, then I don't hate dark chocolate.
If you follow your dreams, then your dreams come true.
If your dreams come true, then you followed your dreams.
If p, then q
If not q, then not p
If angles are congruent, then the measures of the angles are equal.
Identify the inverse.
If angles are not congruent, then the measures of the angles are not equal.
p= You are strong
q= You can flip a car
~q - ~p
If you can't flip a car, then you are not strong.
A man is found dead on Saturday morning. He was killed while his wife was sleeping. The wife tells the police all that she knows. She tells them that the cook was cooking breakfast, the maid was cleaning and the butler was getting the mail. The police immediately arrest the person who is responsible. Who is responsible and why?
The wife because she couldn't have known what everyone was doing if she was sleeping.
P: "It is raining."
Q: "The ground is wet."
R: "I will carry an umbrella."
Q ∨ R
The ground is wet OR I will carry an umbrella.
If Jerimya is not skilled in Call of Duty, then he's K/D ratio is horrific.
If Jerimya is skilled in Call of Duty, then he's K/D ratio is not horrific.
If Alex studied, then he passed the test.
If he passed the test, then Alex studied.
If a student participates in extracurricular activities, then they will develop new skills.
If a student does not develop new skills, then they did not participate in extracurricular activities.
If Sharquisha is ugly, then she needs make up.
Identify the inverse.
If Sharquisha is not ugly, then she does not need makeup
p= The clouds are dark
q= It is going to rain
~p - q
If the clouds are not dark, then it is going to rain.
You have 10 fish, 5 drowned, 3 came back to life. How many fish are alive?
All of them because fish can't drown.
Let P: "The game is close."
Let Q: "Team A is leading."
Let R: "There are only a few minutes left in the game."
Q ∨ R:
P ∧ Q:
Q ∨ R: "Team A is leading or there are only a few minutes left in the game."
P ∧ Q: "The game is close and Team A is leading."
If Drake does not have a better album sales than Kendrick, then Drake is not better the Kendrick.
If Drake have a better album sales than Kendrick, then Drake is better than Kendrick
If a team has a strong defense, then they will limit their opponent's scoring.
If a team limits their opponent's scoring, then they likely have a strong defense.
If a rapper has a Grammy, then they are recognized for their artistry.
If a rapper is not recognized for their artistry, then they do not have a Grammy.
If Isiah is playing baseball, then he needs a bat.
Identify the contrapositive.
If Isiah does not need a bat, then he is not playing baseball.
p= The snow storm is coming
q= People buy tons of food to prepare
~q - ~p
If people don't buy tons of food to prepare, then the snow storm is not coming .
I have streets but no pavement, I have cities but no buildings, I have forests but no trees, I have rivers yet no water. What am I?
A map
P : "There is a superhero with super strength."
Q : "There is a superhero who can fly."
R : "There is a superhero who is invisible."
~Q ∨ R:
P ∧ Q:
~Q ∨ R:There is not a superhero who can fly, or there is a superhero who is invisible.
P ∧ Q:There is a superhero with super strength and there is a superhero who can fly.
If Coach Young is teaching, then Coach Young knows Mr. Blackwell is close by.
If Coach Young is not teaching, then Coach Young does not know Mr. Blackwell is close by
If a student participates in class, then they understand the material.
If a student understands the material, then they participated in class.
If a recipe calls for sugar, then it will be dessert.
If a recipe is not a dessert, then it does not call for sugar.
If 3x does not equal 6, then x does not equal 2.
Identify the converse.
If x does not equal 2, then 3x does not equal 6
P : "I enjoy cooking."
Q : "I cook meals regularly."
~P ∧ ~Q
I do not enjoy cooking, and I do not cook meals regularly.
What Room Number Are We In?
417
P : "I will cook dinner tonight."
Q : "I have all the ingredients."
R : "I will order takeout."
~Q ∨ R
~P ∧ ~Q
~Q ∨ R: I do not have all the ingredients or I will order takeout.
~P ∧ ~Q: I will not cook dinner tonight and I do not have all the ingredients.