Conditional Reasoning I Flashcards
ID the Sufficient Condition Indicator:
If I’m breathing, then air is present
If
ID the Sufficient Condition Indicator:
When I’m breathing, air is present
When
ID the Sufficient Condition Indicator:
Whenever I’m breathing, air is present
Whenever
ID the Sufficient Condition Indicator:
Any breathing requires that air is present
Any
ID the Sufficient Condition Indicator:
All instances of breathing have air present
All
ID the Sufficient Condition Indicator:
Every instance of breathing has air present
Every
ID the Sufficient Condition Indicator:
Everytime I’m breathing, air is present
Everytime
ID the Sufficient Condition Indicator:
In order to breathe, I must have air
In order to
ID the Sufficient Condition Indicator:
People who breathe need air
People who
ID the Sufficient Condition Indicator:
Each instance of breathing requires air
Each
Vocabulary Question:
What is the sufficient condition?
The sufficient condition is the “if” part of the conditional statement.
Conditional statements rely on if -> then logic.
Vocabulary Question:
What does it mean to activate a conditional?
It means that the sufficient condition (if condition) is present, and therefore must be followed.
if we can say “yes” to the “if” statement, we’re activating it.
Vocabulary Question:
What is the necessary condition?
The “then” part of the conditional statement is called the necessary condition.
Conditional statements rely on if -> then logic.
ID the Necessary Condition Indicator:
If I’m breathing, then air is present
Then
Necessary condition indicator is the “then” word
ID the Necessary Condition Indicator:
Air must be present for breathing.
must
ID the Necessary Condition Indicator:
Air is necessary for breathing.
necessary
ID the Necessary Condition Indicator:
Air is required for breathing.
required
ID the Necessary Condition Indicator:
Only the presence of air allows for breathing.
Only
ID the Necessary Condition Indicator:
Breathing depends on air being present
depends
ID the Necessary Condition Indicator:
I need air to breathe
need
ID the Necessary Condition Indicator:
I have to have air if I’m breathing
Have to
ID the Necessary Condition Indicator:
Air is essential for breathing
essential
ID the Necessary Condition Indicator:
Air is a precondition for breathing
precondition
ID the Necessary Condition Indicator:
I’m breathing, only if air is present
only if
Pay special attention to ONLY IF. It is a necessary indicator, even though it contains the word “if”. You can think of it like the word “only” is dominant over the word “if”
Vocabulary:
What is the “Must Relationship”
The must realtionship states that if the sufficient condition occurs, the necessary condition must occur.
ID what gets activated in the conditional statement:
Sufficient condition is present
The sufficient condition is the “if” condition.
Activate the sufficient condition. What happens next?
The necessary condition must occur.
The necessary condition is the “then” condition
*If I’m breathing, then air is present. *
In this scenario, the sufficient condition is present.
*I’m breathing! *
So what happens next? I’m breathing, so air MUST be present.
B -> A
ID what gets activated in the conditional statement:
Necessary condition is absent
The necessary condition is the “then” condition.
We know the necessary condition is not happening. What happens next?
/necessary condition -> ?
We can’t have the sufficient condition.
The sufficient condition is the “if” condition
If I’m breathing, air is present.
In this scenario, the necessary condition is **missing. **
There’s no air, so I can’t breathe!!
So what happens next? There’s no air, so I’m not breathing.
/A -> /B
ID what gets activated in the conditional statement:
Sufficient condition is absent
The sufficient condition is the “if” condition
Nothing gets activated.
If I’m breathing, air is present.
B -> A
The sufficient condition is absent.
I’m not breathing
In this scenario, we don’t have a sufficient condition to start us off, because we’re mssing the sufficient condition.
*There’s no breathing happening, so we don’t know anything else. *
So what happens next? Nothing, this is an incomplete conditional statement.
In order for us to know what happens next, we would need a sufficient condition that leads to breathing being a necessary condition in a conditional chain, and we don’t have that here.
ID what gets activated in the conditional statement:
The necessary condtition is present
The necessary condition is the “then” condition
Nothing gets activated.
If I’m breathing, air is present.
B -> A
The necessary condition is present.
air is present
In this scenario, we have the necessary condition but are missing the sufficient condition to start us off. So all we know is that there is air but nothing else.
ID how to represent the must relationship symbolliclly:
Sufficient condition goes on the (left/right) side of the must arrow, (before/after) the must arrow.
sufficient condition is the “if” condition
left, before
the must relationship always goes if-> then
ID how to represent the must relationship symbolliclly:
Necessary condition goes on the (left/right) side of the must arrow, (before/after) the must arrow.
necessary condition is the “then” condition
right, after
the must relationship always goes if-> then
ID the contrapositive:
A->B
The contrapositive is the flipped and negated conditional
~B -> ~A
ID the contrapositive:
Q -> ~R
The contrapositive is the flipped and negated conditional
R - > ~Q
ID the contrapositive:
~L -> P
The contrapositive is the flipped and negated conditional
~P - > L
ID the contrapositive:
~Y -> ~X
X -> Y
