Inverse/ Converse/ Contrapositive
The inverse of the conditional statement "If it rains, then the ground is wet" is this.
What is "If it does not rain, then the ground is not wet"?
This phrase introduces the "if" part of a conditional statement.
What is the hypothesis?
This is the logical operator symbolized by "∧", combining two statements that must both be true.
What is conjunction?
If you study hard, then you will pass the test. If you pass the test, then you will celebrate. By the Law of Syllogism, what can you conclude?
What is "If you study hard, then you will celebrate"?
If you have 5 apples and add 3 more, then subtract 3, how does this demonstrate the property that adding and then subtracting the same number leaves the original amount?
What is the Addition and Subtraction Property of Equality?
The converse of "If a figure is a square, then it has four equal sides" is this statement.
What is "If a figure has four equal sides, then it is a square"?
In the statement "If it is sunny, then we will go to the park," this part is called the conclusion.
What is "we will go to the park"?
This operator, symbolized by "∨", joins two statements where only one needs to be true.
What is disjunction?
If it rains, then the ground gets wet. If the ground gets wet, then the soccer game will be canceled. What does the Law of Syllogism say about rain and the soccer game?
What is "If it rains, then the soccer game will be canceled"?
If you know that x=7, then multiplying both sides by 2 keeps the equality true. What property is this?
What is the Multiplication Property of Equality?
The contrapositive of "If a number is even, then it is divisible by 2" is this.
What is "If a number is not divisible by 2, then it is not even"?
A conditional statement "If P, then Q" is false only when this happens with P and Q.
What is when P is true and Q is false?
Write the conjunction statement for: "It is raining" (P) and "It is cold" (Q).
What is " It is raining and It is cold"?
f you eat healthy, then you will feel energetic. You eat healthy every day. What can you conclude by the Law of Detachment?
What is "You will feel energetic"?
This property states that any quantity is equal to itself, like saying 7=7.
What is the Reflexive Property of Equality?
The inverse of "If a plant has flowers, then it produces seeds" is often not true. What is the inverse statement?
What is "If a plant does not have flowers, then it does not produce seeds"?
Birds have feathers. Penguins are birds. The conditional statement of these statements is.
What is "If an penguin is a bird, then it has feathers."?
Write the disjunction statement for: "I will study" (P) "I will watch TV" (Q).
If the traffic light is green, then you can go. The traffic light is green. What does the Law of Detachment conclude?
What is "You can go"?
If a=b and b=c, then this property lets you conclude a=c.
What is the Transitive Property of Equality?
The contrapositive of "If a shape is a rectangle, then it has four right angles" must be true. What is the contrapositive?
What is "If a shape does not have four right angles, then it is not a rectangle"?
To pass the test, a student must score at least 60%. The conditional statement is this.
What is "If a student scores at least 60%, then they pass the test." ?
You will get a reward if you finish your homework and clean your room. Write the conjunction statement representing this condition.
What is "If you finish your homework and clean your room, then you get a reward"?
If you get a good grade, then you will get a prize. If you get a prize, then you will be happy. You got a good grade. Using both laws, what can you conclude?
What is "You will be happy"?
When you know x=4, this property allows you to replace x with 4 in any expression.
What is the Substitution Property of Equality?