Conditional Reasoning I

Question 1

ID the Sufficient Condition Indicator:

If I’m breathing, then air is present

Answer 1

If

Question 2

ID the Sufficient Condition Indicator:

When I’m breathing, air is present

Answer 2

When

Question 3

ID the Sufficient Condition Indicator:

Whenever I’m breathing, air is present

Answer 3

Whenever

Question 4

ID the Sufficient Condition Indicator:

Any breathing requires that air is present

Answer 4

Any

Question 5

ID the Sufficient Condition Indicator:

All instances of breathing have air present

Answer 5

All

Question 6

ID the Sufficient Condition Indicator:

Every instance of breathing has air present

Answer 6

Every

Question 7

ID the Sufficient Condition Indicator:

Everytime I’m breathing, air is present

Answer 7

Everytime

Question 8

ID the Sufficient Condition Indicator:

In order to breathe, I must have air

Answer 8

In order to

Question 9

ID the Sufficient Condition Indicator:

People who breathe need air

Answer 9

People who

Question 10

ID the Sufficient Condition Indicator:

Each instance of breathing requires air

Answer 10

Each

Question 11

Vocabulary Question:

What is the sufficient condition?

Answer 11

The sufficient condition is the “if” part of the conditional statement.

Conditional statements rely on if -> then logic.

Question 12

Vocabulary Question:

What does it mean to activate a conditional?

Answer 12

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.

Question 13

Vocabulary Question:

What is the necessary condition?

Answer 13

The “then” part of the conditional statement is called the necessary condition.

Conditional statements rely on if -> then logic.

Question 14

ID the Necessary Condition Indicator:

If I’m breathing, then air is present

Answer 14

Then

Necessary condition indicator is the “then” word

Question 15

ID the Necessary Condition Indicator:

Air must be present for breathing.

Answer 15

must

Question 16

ID the Necessary Condition Indicator:

Air is necessary for breathing.

Answer 16

necessary

Question 17

ID the Necessary Condition Indicator:

Air is required for breathing.

Answer 17

required

Question 18

ID the Necessary Condition Indicator:

Only the presence of air allows for breathing.

Answer 18

Only

Question 19

ID the Necessary Condition Indicator:

Breathing depends on air being present

Answer 19

depends

Question 20

ID the Necessary Condition Indicator:

I need air to breathe

Answer 20

need

Question 21

ID the Necessary Condition Indicator:

I have to have air if I’m breathing

Answer 21

Have to

Question 22

ID the Necessary Condition Indicator:

Air is essential for breathing

Answer 22

essential

Question 23

ID the Necessary Condition Indicator:

Air is a precondition for breathing

Answer 23

precondition

Question 24

ID the Necessary Condition Indicator:

I’m breathing, only if air is present

Answer 24

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”

Question 25

Vocabulary:

What is the “Must Relationship”

Answer 25

The must realtionship states that if the sufficient condition occurs, the necessary condition must occur.

Question 26

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?

Answer 26

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

Question 27

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 -> ?

Answer 27

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

Question 28

ID what gets activated in the conditional statement:

Sufficient condition is absent

The sufficient condition is the “if” condition

Answer 28

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.

Question 29

ID what gets activated in the conditional statement:

The necessary condtition is present

The necessary condition is the “then” condition

Answer 29

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.

Question 30

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

Answer 30

left, before

the must relationship always goes if-> then

Question 31

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

Answer 31

right, after

the must relationship always goes if-> then

Question 32

ID the contrapositive:

A->B

The contrapositive is the flipped and negated conditional

Answer 32

~B -> ~A

Question 33

ID the contrapositive:

Q -> ~R

The contrapositive is the flipped and negated conditional

Answer 33

R - > ~Q

Question 34

ID the contrapositive:

~L -> P

The contrapositive is the flipped and negated conditional

Answer 34

~P - > L

Question 35

ID the contrapositive:

~Y -> ~X

Answer 35

X -> Y