Conditional Statement
What is the conclusion in this sentence: If a figure is a rectangle, then it has four right angles.
It has four right angles
If two angles are adjacent, then they share a side.
Write on the board the symbols for AND, OR, Therefore (in that order).
^^^ vvv :.
Give two laws of deductive reasoning.
Law of Detachment and Law of Syllogism
Identify the hypothesis in this statement: If you buy this phone case, you will get a 5% discount.
You buy this phone case.
State the inverse: If the date is July 4, then it is Independence Day.
If the date is not July 4, then it is not Independence Day.
What conditional statement does this symbol represent:
q->p
converse of a conditional statement
Which law is being described: If p -> q is true and p is true, then q is true.
Law of Detachment
Provide a counter example for this conditional statement: If a beverage is generally served hot, then it is coffee.
The beverage can be hot chocolate (or any hot drink other than coffee like tea)
State the contrapositive: If a figure has ten sides, then it is a decagon.
If a figure is not a decagon, then it does not have 10 sides.
Given:
p: it is an animal
q: it is a dog
r: it is a golden retriever
Write the symbolic translation of: It is an animal and it is not a dog.
p^^^~q
If an angle measures less than 90 degrees, it is an acute angle. Angle X measures 89 degrees. What conclusion can you make?
Angle X is an acute angle.
Write as a conditional statement: A six-sided polygon is a hexagon.
If a polygon is six-sided, then it is a hexagon.
State the biconditional: If a figure is a line segment, then it is a straight line with two endpoints.
A figure is a line segment if and only if it is a straight line with two endpoints.
Given:
p: the speed limit is 45 mph
q: I did not get a speeding ticket
r: I drove fast
What is the written translation of
~qharr r
I get a speeding ticket if and only if I drove fast.
Which law was used to make a conclusion?
If two base angles of a triangle are congruent, then the triangle has two congruent sides. ∆𝐴𝐵𝐶 has two congruent base angles. ∴ ∆𝐴𝐵𝐶 has two congruent sides
Law of Detachment
Provide a counterexample: If a number is divisible by 3, then it is odd.
18 is divisible by 3 and it is even.
Explain clearly how to state the contrapositive of a conditional statement.
Switch the hypothesis and conclusion, then state the negation of both.
Given:
p: the speed limit is 45 mph
q: I did not get a speeding ticket
r: I drove fast
(p^^^q)->~r
If the speed limit is 45mph and I did not get a speeding ticket, then I did not drive fast.
If a line intersects a segment at its midpoint, then the line bisects the segment. If a line bisects a segment, then it divides the segment into two congruent segments. Make a conclusion and state which law you used to make that conclusion.
If a line intersects a segment at its midpoint, then it divides the segment into two congruent segments. Law of Syllogism