Logic Cheat Sheet, Translating Logical Operators

Question 1

If A, then B

Answer 1

A→B

Question 2

If not B, then not A

Answer 2

not B→not A
contrapositive: A→B

Question 3

All As are Bs

Answer 3

A→B

Question 4

A only if B

Answer 4

A→B

Question 5

Not A unless B

Answer 5

A→B

Question 6

Not A until B

Answer 6

A→B (not until = only)

Question 7

Only B can be A

Answer 7

A→B

Question 8

The only way to do A is to do B

Answer 8

A→B

Question 9

A depends on B

Answer 9

A→B

Question 10

None but B are A

Answer 10

A→B (none but = only)

Question 11

None except B are A

Answer 11

A→B (none except = only)

Question 12

Not until B can I do A

Answer 12

A→B

Question 13

If A, then not B

Answer 13

A→not B

Question 14

If B, then not A

Answer 14

A→not B

B→not A

Question 15

No A are B

Answer 15

A→not B
(No= negate necessary)

Question 16

No B are A

Answer 16

A→not B

Question 17

Cannot have both A and B

Answer 17

A→not B

Question 18

A depends on not B

Answer 18

A→not B

Question 19

B depends on not A

Answer 19

A→not B

Question 20

A only if not B

Answer 20

A→not B

Question 21

B only if not A

Answer 21

A→not B

Question 22

At most one of A or B is selected

Answer 22

A→not B

Question 23

At least one of A or B is not selected

Answer 23

A→not B

Question 24

If not A, then B

Answer 24

not A→ B

Question 25

If not B, then A

Answer 25

not A→ B

Question 26

Without A, we must have B

Answer 26

not A→ B
(Without = negate sufficient)

Question 27

Without B, we must have A

Answer 27

(not B→ A)

Question 28

At least one of A or B is selected

Answer 28

not A→ B

Question 29

At most one of A or B is not selected

Answer 29

not A→ B

Question 30

Either A or B is selected

Answer 30

not A→ B

Question 31

If A then B, and if B then A

Answer 31

A ↔ B

Question 32

A and B are interdependent

Answer 32

A ↔ B

Question 33

All As are B and all B are A

Answer 33

A ↔ B

Question 34

A if and only if B

Answer 34

A ↔ B

Question 35

B if an only if A

Answer 35

A ↔ B

Question 36

Cannot have A without B, and cannot have B without A

Answer 36

A ↔ B

Question 37

Either A and B are selected, or else neither A nor B are selected

Answer 37

A ↔ B

Question 38

Either A or B, but not both, is selected

Answer 38

A ↔ not B

Question 39

All except A are B

Answer 39

A ↔ not B
(biconditional, negate necessary)

Question 40

All except B are A

Answer 40

A ↔ not B

All except = forever apart, bi-conditional

Question 41

All but A are B

Answer 41

A ↔ not B

(biconditional, negate necessary)

Question 42

All but B are A

Answer 42

A ↔ not B

(biconditional, negate necessary)

Question 43

All except B are A

Answer 43

A ↔ not B

Question 44

All but A are B

Answer 44

A ↔ not B

Question 45

All but B are A

Answer 45

A ↔ not B

Question 46

A if and only if not B

Answer 46

A ↔ not B

If and only if not= forever apart biconditional

Question 47

B if and only if not A

Answer 47

A ↔ not B

Question 48

Either A is selected without B, or else B is selected without A

Answer 48

A ↔ not B

Question 49

Either A is selected and B is not selected, or else B is selected and A is not selected

Answer 49

A ↔ not B

Question 50

If A, then neither B nor C

Answer 50

A→ not B and not C

Question 51

B is in any photo that A is in

Answer 51

A→ B

Question 52

A unless B

Answer 52

Not A→B

Question 53

Unless A, then B

Answer 53

Not A→B

Question 54

No A without B

Answer 54

A →B

Question 55

No A unless B

Answer 55

A →B