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WorksheetsInductive Reasoning, Conditionals (Converses, Bi-Conditionals), Deductive Reasoning, and Algebraic Proofs
Total questions: 40
Worksheet time: 29mins
Inductive reasoning is reasoning based on the following:
patterns and observations
given facts
how to solve an equation
given statements
Deductive reasoning is reasoning based on the following:
patterns and observations
given facts and statements
how to solve an equation
prior knowledge
A ________ is a conclusion reached using inductive reasoning.
counterexample
conjecture
hypothesis
conditional
To prove a conjecture is false you must provide a __________.
conjecture
hypothesis
counterexample
converse
A ____________ is a statement that can be written in if-then form.
converse
conclusion
bi-conditional
conditional
The _______________ of a conditional is the phrase immediately following the word if.
conclusion
converse
switch
hypothesis
The _______________ of a conditional is the phrase immediately following the word then.
conclusion
converse
switch
hypothesis
The converse of a conditional is formed by ____________ the hypothesis and conclusion.
deleting
switching
copying
negating
A ____________ is the combination of a conditional and its converse.
bi-conditional
statement
conjecture
counterexample
To use the Law of Detachment, the given information must contain ____________ conditional (if-then) statements.
0
1
2
4
To use the Law of Syllogism, the given information must contain ____________ conditional (if-then) statements.
0
1
2
4
-3, 6, -12, 24, ...
What is the hypothesis of the following statement:
"If Johnny is late to school, then his mom will have to drive him."
His mom will have to drive him
late to school
Johnny is late to school
Then his mom will have to drive him
Given the conditional;
"If Jose eats fish, then he has an allergic reaction"
Which of the following is the converse?
None of these
If Jose doesn't have an allergic reaction, then he didn't eat fish.
If Jose doesn't eat fish, then he doesn't have an allergic reaction.
If Jose has an allergic reaction, then he ate fish.
Given the conditional;
"If Destiny goes to work tonight, then she will make money"
What is the conclusion?
Destiny goes to work tonight
Destiny doesn't go to work
She will make money
then she will make money
If a figure has four sides, then it is a square.
Which of these is a counterexample to the following statement?
All farm animals have four legs.
Cows
Penguins
Elephants
Chickens
Which of these is a counterexample to the following statement?
All vegetables are green.
Banana
Pumpkins
Green Beans
Grass
When writing a biconditional statement, we use the phrase ___ between the hypothesis and conclusion.
if
then
if and only if
always
What counterexample makes the following biconditional false?
"It is Halloween if and only if it is October 31."
This is a true biconditional, so it has no counterexamples.
It is not October 31.
I don't celebrate Halloween.
It is October 30.
Identify the symbolic notation: p---->q
conditional
converse
bi-conditional
Identify the symbolic notation: p<---->q
conditional
converse
bi-conditional
Identify the symbolic notation: q---->p
conditional
converse
bi-conditional
Given: If an animal is a dog, then they like biscuits.
Sammy is a dog.
Conclusion: Sammy likes biscuits.
Statement 1: If you exercise regularly, then you have a healthy body
Statement 2: If you have a healthy body, then you have more energy
Statement 1: If I study for one hour each day, then I will score well on the exam
Statement 2: I will score well on the exam
If this wind keeps up, then we will lose some trees. We lose some trees.
Andy concludes that the wind keeps up.
Is he correct?
Yes, by the Law of Detachment.
No; the Law of Detachment doesn't work here because we weren't told the hypothesis was true.
p
∴ q
Which law of logic?
q → r
∴ p → r
Which law of logic?
