Logic Cheat Sheet, Translating Logical Operators Flashcards
(55 cards)
1
Q
If A, then B
A
A→B
2
Q
If not B, then not A
A
not B→not A
contrapositive: A→B
3
Q
All As are Bs
A
A→B
4
Q
A only if B
A
A→B
5
Q
Not A unless B
A
A→B
6
Q
Not A until B
A
A→B (not until = only)
7
Q
Only B can be A
A
A→B
8
Q
The only way to do A is to do B
A
A→B
9
Q
A depends on B
A
A→B
10
Q
None but B are A
A
A→B (none but = only)
11
Q
None except B are A
A
A→B (none except = only)
12
Q
Not until B can I do A
A
A→B
13
Q
If A, then not B
A
A→not B
14
Q
If B, then not A
A
A→not B
B→not A
15
Q
No A are B
A
A→not B
(No= negate necessary)
16
Q
No B are A
A
A→not B
17
Q
Cannot have both A and B
A
A→not B
18
Q
A depends on not B
A
A→not B
19
Q
B depends on not A
A
A→not B
20
Q
A only if not B
A
A→not B
21
Q
B only if not A
A
A→not B
22
Q
At most one of A or B is selected
A
A→not B
23
Q
At least one of A or B is not selected
A
A→not B
24
Q
If not A, then B
A
not A→ B
25
If not B, then A
not A→ B
26
Without A, we must have B
not A→ B
(Without = negate sufficient)
27
Without B, we must have A
(not B→ A)
28
At least one of A or B is selected
not A→ B
29
At most one of A or B is not selected
not A→ B
30
Either A or B is selected
not A→ B
31
If A then B, and if B then A
A ↔ B
32
A and B are interdependent
A ↔ B
33
All As are B and all B are A
A ↔ B
34
A if and only if B
A ↔ B
35
B if an only if A
A ↔ B
36
Cannot have A without B, and cannot have B without A
A ↔ B
37
Either A and B are selected, or else neither A nor B are selected
A ↔ B
38
Either A or B, but not both, is selected
A ↔ not B
39
All except A are B
A ↔ not B
(biconditional, negate necessary)
40
All except B are A
A ↔ not B
All except = forever apart, bi-conditional
41
All but A are B
A ↔ not B
(biconditional, negate necessary)
42
All but B are A
A ↔ not B
(biconditional, negate necessary)
43
All except B are A
A ↔ not B
44
All but A are B
A ↔ not B
45
All but B are A
A ↔ not B
46
A if and only if not B
A ↔ not B
If and only if not= forever apart biconditional
47
B if and only if not A
A ↔ not B
48
Either A is selected without B, or else B is selected without A
A ↔ not B
49
Either A is selected and B is not selected, or else B is selected and A is not selected
A ↔ not B
50
If A, then neither B nor C
A→ not B and not C
51
B is in any photo that A is in
A→ B
52
A unless B
Not A→B
53
Unless A, then B
Not A→B
54
No A without B
A →B
55
No A unless B
A →B
