Conditional
Make a conditional statement for John, who always goes out to run but not on a rainy day.
If John is running, then it's not a rainy day.
What is the converse of the sentence below?
If it's a Saturday, then I can bike in the park
If I can bike in the park, then it's a Saturday
Which of the following is an Inverse statement?
A. if b, then a
B. if not b, then not a
C. if not a, then not b
D. if not a, then b
C
What is the contrapositive of this inverse statement
If humans do not drink water for 3 days, then they will not survive.
If humans do not survive, then they will not drink water for 3 days.
True or false? If false, provide a counterexample
If I am sitting down, then I cannot be standing up
True, no counterexample needed
Make a conditional statement about someone who tells a lie, and the nose grows
If you tell a lie, then your nose will grow
What is the converse of this statement below, and if the converse is true/false?
If a number is divisible by 5, then its final digit is a 0
Converse
If a number's final digit is a 0, then it's divisible by 5
This is true.
What is the inverse of this statement
"If I am swimming in the ocean, then I am swimming in salt water."?
If I am NOT swimming in the ocean, then I am NOT swimming in salt water
Which of the following is the contrapositive of this statement: "If I am a Canadian, then I enjoy hockey."
A. If I am not a Canadian, then I do not enjoy hockey.
B. If I do not enjoy hockey, then I am not a Canadian.
C. If I enjoy hockey, then I am a Canadian.
D. If I am an American, then I enjoy basketball.
B
Contrapositive is the NOT statement of the converse
Conver=if I enjoy hockey, then I am a Canadian
Provide a counterexample if the statement is false
If it's a sunny day, then you bike to school.
False
You can walk, run, ride a car, etc
What is the conditional statement if the inverse is
if a plant does not get the sunlight, then it will not grow well?
if a plant gets the sunlight, then it grows well.
Write a converse statement for this sentence.
The conditional statement would be:
If it's an equilateral triangle, then it has three equal sides.
The converse statement would be:
If it has three equal sides, then it's an equilateral triangle.
Is the inverse of this statement, "if you are over 16, then you can drive", true or false? Explain
Inverse: If you are NOT over 16, then you CANNOT drive a car
False because some people are driving at the age of 15.
The Statement "If n is a natural number, then 2n is an even number.",
Has a contrapositive statement. 1. Write the contrapositive statement. 2. Is the contrapositive statement true or false? Explain
Converse: 2n is an even number, then n is a natural number
Contrapositive: If 2n is NOT an even number, then n is NOT a natural number
This is true because if the conditional statement is true, then the contrapositive must be true.
bi-conditional (statement)
Make a conditional statement:
A school is considering switching to a four-day school week to reduce costs and give students more time for rest and extracurricular activities. Some parents are concerned about childcare and learning loss, while others support the idea for its flexibility.
If the school switches to a four-day work week, then students might have more time to rest and pursue hobbies, but they could also fall behind academically if the curriculum isn’t adjusted properly.
What is the converse of
"If the square root of (X square) is equal to x, then x is not negative."
And is this true? Why/why not?
Converse,
If x is not negative, then the square root of x square is equal to x
The conditional statement is false, because a negative number square is also positive, eg (-2)^2=4, and the square root of 4 = 2
Help Sarah write an inverse statement to find the missing side of a right triangle (hint: using a special theorem??!!).
Conditional: If it's a right triangle, then I can use the Pythagorean theorem to find the missing sides.
Inverse: If it's NOT a right triangle, then I CANNOT use the Pythagorean theorem to find the missing sides.
Scenario:
At a company, employees are only allowed to work remotely if they have completed cybersecurity training. This policy is in place to ensure data protection while working off-site.
Write the contrapositive statement, then determine whether the contrapositive is true or false, and explain your reasoning based on the scenario.
The Conditional statement:
“If an employee has completed cybersecurity training, then they are allowed to work remotely.”
The Contrapositive statement:
"If employees are NOT allowed to work remotely, then they have NOT completed cybersecurity training."
Meridith wrote the following statement
"A quadrilateral is a parallelogram if and only if its opposite sides are parallel"
and said that this is a biconditional, is she correct? Explain
No, she is not because the converse is not true.
The converse of this statement would be
"If a quadrilateral's opposite sides are parallel, then it's a parallelogram.",
which is false, because it can be a rectangle or square, too.