Validity

Question 1

If the premises are true, then the conclusion must be true

Answer 1

If the premises are true, then the conclusion must be true

Question 2

Truth

Answer 2

sentences

Question 3

valid

Answer 3

arguments

Question 4

Valid argument 1: affirming the sufficient

Answer 4

a > b
a
\_\_\_\_\_\_\_\_
b 
if affirm the sufficient condition, then you conclude the necessary condition.

Question 5

Valid argument 2: negating the necessary

Answer 5

a > b
/b
______
/a

Question 6

Valid argument 3:

Answer 6

a > b > c
_______
a > c

a > b
b > c
_____
a > c

Question 7

Some

Many = Some

Answer 7

at least one
ranges from 1 to 100
a b
a some b

these don’t have contrapositives

Question 8

All

Answer 8

speaks of a point = 100

Question 9

Most

Answer 9

more than half
means half plus 1 = 51 and upper bound is 100

a most b

• doesn’t have a contrapositive

Question 10

Few

Answer 10

= some are

= most are not

Question 11

All implies Most implies Some

Answer 11

0_________50________100
Some (at least 1_________
but it goes up to “all”)
Few(some are and most are not)
+1 Most_____
All

Question 12

The existential quantifier is a fancy name to express the relationship of intersections. The three logical indicators here are “some” which means at least 1 up to all; “most” which means half plus 1 up to all; and “few” which usually means some are and most are not.

Answer 12

The existential quantifier is a fancy name to express the relationship of intersections. The three logical indicators here are “some” which means at least 1 up to all; “most” which means half plus 1 up to all; and “few” which usually means some are and most are not.

Question 13

The SOME group

Answer 13

some, many, several, at least one, lots, not none

Question 14

The Most group

Answer 14

most, a majority, more than half

Question 15

Few

Answer 15

Few

Question 16

These have no contrapositives

Answer 16

No contrapositives

Question 17

Negations

Answer 17

Negations

Question 18

Negate SOME statements

Answer 18

some = none

Question 19

Negate ALL

Answer 19

all = some not

Question 20

The easiest way to get the contradiction of any sentence is to tag the clause “It’s not the case that…” in front of the sentence.

Answer 20

“It’s not the case that…”

Question 21

A is not sufficient for B and B is not necessary for A

Answer 21

A is not sufficient for B and B is not necessary for A

Question 22

You can formulate the contradiction (i.e., the negations) by saying “Some [of the sufficient] is not [the necessary].” Or, if grammatically it doesn’t make sense to use “some,” you can fall back on the more general rule of “One can be [the sufficient] and not be [the necessary].” For example, “If the President endorses this bill, then it will pass.” Here, it clearly doesn’t make sense to use “some.” So, we fall back on the more general rule and say “The President can endorse the bill and it could not pass.”

Answer 22

You can formulate the contradiction (i.e., the negations) by saying “Some [of the sufficient] is not [the necessary].” Or, if grammatically it doesn’t make sense to use “some,” you can fall back on the more general rule of “One can be [the sufficient] and not be [the necessary].” For example, “If the President endorses this bill, then it will pass.” Here, it clearly doesn’t make sense to use “some.” So, we fall back on the more general rule and say “The President can endorse the bill and it could not pass.”

Question 23

All negates - some not

Answer 23

ALL negates - some not

Question 24

Some negate - none

Answer 24

Some negate - none

Question 25

To negate slap in front of the sentence - It’s not the care that ….

Answer 25

To negate slap in front of the sentence - It’s not the care that ….

Question 26

Valid argument 4:

Answer 26

A some > B >(all) C
__________
A some C

Question 27

Valid argument 5:

Answer 27

A most > B >(all) C
____________
A most C

Question 28

Valid Argument 6:

Answer 28

A > (all) B > (all) C
_____________
A some C

Question 29

Valid Argument 7:

Answer 29

A > B
A some C
______
B some C

Question 30

Valid Argument 8:

Answer 30

A > B
B most C
______
A some C