If-Then Statements
Write this as a conditional: "All rectangles have four sides"
If a shape is rectangle, then it has four sides.
What's the inverse of "If it's sunny, then it's warm"?
What phrases connects a biconditional statement in the middle?
"If and only if."
Inductive.
Find the next term and state a conjecture: 2, 4, 6, 8, ...
Next term: 10; Conjecture: Numbers increase by 2.
Identify the hypothesis: "If it rains, then the ground gets wet."
It rains.
What's the contrapositive of "If you are a teenager, then you are under 20"?
If you are not under 20, then you are not a teenager.
Turn this into a biconditional statement. "If a figure is a square, then it has four congruent sides."
"A figure is a square if and only if it has four congruent sides."
Inductive or deductive: "All squares are rectangles; therefore a 4x4 shape is a rectangle."
Deductive.
Find the next term and state a conjecture: 1, 1, 2, 3, 5, ...
Next term: 8; Conjecture: The next number in the sequence is the sum of the previous two.
Identify the conclusion: "If you study, then you will pass the test."
You will pass the test.
Name two statements that always have the same truth value.
Conditional & Contrapositive. OR Converse & Inverse.
True or False: "A triangle is isosceles if and only if it has two equal sides."
True
What law is being applied here?
If it rains, then the ground will get wet.
It rained.
The ground got wet.
True or False: "If one example proves a conjecture wrong, the conjecture if false."
True.
Write the converse of: "If it's a square, then it's a rectangle."
If it's a rectangle, then it's a square.
True of False: The converse and inverse always have the same truth value.
True.
Explain why "A number is even if and only if it's divisible by 2" is a valid biconditional.
Both the conditional and converse are true.
What is the conclusion? If invalid, please state so.
"If it rains, the ground gets wet. If the ground gets wet, the game is canceled."
Give a counterexample to: "All quadrilaterals are rectangles."
A trapezoid or rhombus.
True or false: "If an angle is obtuse, then it measures more than 90 degrees."
True
Write a conditional and all three related statements correctly.
Answers Vary.
Write a conditional statement and its converse that cannot result in a biconditional statement.
Answers vary.
What is the conclusion. If invalid, please state so.
If Johnny exercises, then he will make the track team.
Johnny does not exercise.
Invalid.
What is a conjecture?
An educated guess based on patterns or observations.