Sufficient and Necessary

Question 1

the first part of a SN diagram is

Answer 1

the sufficient side

Question 2

the second part of a SN diagram is

Answer 2

the necessary side

Question 3

how do you contrapose for General Principle

Answer 3

flip the variables and negate them

Question 4

T/F you can never conclude the sufficient condition using the general principle

Answer 4

true

Question 5

what is the general principle

Answer 5

invoking sufficient to conclude the necessary

Question 6

sufficient

Answer 6

a condition (x) is said to be sufficient for another condition (y) if (and only if) the truth / existence / occurrence of x guarantees or brings about the truth / existence / occurrence of y

Question 7

we can conclude a necessary condition

Answer 7

if we have sufficient one

Question 8

necessary

Answer 8

a condition (y) is said to be necessary for another condition (x) if (and only if) the falsity / nonexistence / nonoccurrence of x

Question 9

contrapositive must

Answer 9

be true

Question 10

if something is necessary and is missing then

Answer 10

we can’t have the sufficient condition

Question 11

if statements rule

Answer 11

if introduces a sufficient condition. the other part of the sentence is the necessary condition

Question 12

what are other words that can be diagrammed like if (introduce the sufficient condition)

Answer 12

when, where, wherever, whenever

Question 13

only if statements rule

Answer 13

only if introduces a necessary condition. the other part of the statement is the sufficient condition

Question 14

what other words can be diagrammed like only if (introduce a necessary condition)

Answer 14

only when, only where

Question 15

only statements rule

Answer 15

only introduces a necessary condition. the other part of the statement is the sufficient condition.

Question 16

“the only” statements rule

Answer 16

“the only” introduces a sufficient condition. the other part of the sentence is necessary.

Question 17

if and only if statements rule

Answer 17

“if and only if” indicates that each variable is both a sufficient and necessary condition. “if and only if” is diagrammed with a double arrow

Question 18

another wording that is diagrammed like if and only if

Answer 18

if but only if

Question 19

all statements rule

Answer 19

all introduces a sufficient condition. the other part of the statement is the necessary condition

Question 20

what other words are diagrammed like all (introduce sufficient)

Answer 20

every, each, any

Question 21

people who statements rule

Answer 21

“people who” introduces a sufficient condition. the other part is a necessary condition

Question 22

no statements rule

Answer 22

the statement “no Xs are Ys” means that something cannot be both X and Y or stated another way, X and Y are mutually exclusive.

Question 23

how to diagram no statements

Answer 23

Step 1: pick a variable and make it the sufficient condition
Step 2: negate the other variable and make it a necessary condition

Question 24

not both is diagrammed like

Answer 24

no

Question 25

for no statements what is possible and impossible

Answer 25

both variables cannot be true, both variables can be false

Question 26

either or statements rule

Answer 26

the statement “either x or y” means that at least one of x or y must exist

Question 27

how to diagram either or statements

Answer 27

Step 1: pick a variable and make it necessary
Step 2: negate the other variable and make it the sufficient condition

Question 28

for either or statements what must be true

Answer 28

at least one variable must exist, but both can

Question 29

unless statements rule

Answer 29

Step 1: unless introduces a necessary condition, which means that the part of the sentence that follows will be the necessary condition
Step 2: negate the other part of the sentence and make it the sufficient condition

Question 30

what is diagrammed like unless

Answer 30

without, until

Question 31

compound statements are

Answer 31

and/or

Question 32

compound statements rule

Answer 32

converting a compound statement into its contrapositive requires converting every “or” to “and” and every “and” to “or”

Question 33

transitive property

Answer 33

A -> B -> C -> D
therefore A -> D

Question 34

what is a rule of the transitive property

Answer 34

you cannot go back in the chain
if you are asked about B, you can conclude C, D but not A

Question 35

when doing a question, you must

Answer 35

ALWAYS WRITE THE CONTRAPOSITIVE