Logical Symbols
Symbol | Name | Explanation |
---|---|---|
∀ | Universal Quantification | ∀x P(x) means P(x) is True for all x. |
∃ | Existential Quantification | ∃x P(x) means there is at least one x such that P(x) is True. |
∧, &, · | Conjunction | A ∧ B is True if A and B are both True, otherwise it is False. |
∨, |, + | Disjunction | A ∨ B is True if A or B (or both) are True, otherwise it is False. |
⇒, →, ⊃ | Material Implication | A ⇒ B is False only when A is True and B is False, otherwise it is True. |
⇔, ≡, ↔ | Material Equivalence (Biconditional) | A ⇔ B is True only when both A and B are False, or both A and B are True. |
¬, ~, ! | Negation | ¬A is True if and only if A is False. |
⊕ | Exclusive Disjunction | A ⊕ B is True when either A or B is True, but not both. |
⊢ | Derives | x ⊢ y means y is provable from x |
Set Symbols
Symbol | Name | Explanation |
---|---|---|
{ } | Set | An unordered collection of elements |
| | Such that | Used in set builder notation to stand for "such that" |
A∩B | Intersection | Elements in both sets A and B. |
A∪B | Union | Elements in set A or set B (inclusively). |
A⊆B | Subset | Every element in A is in B. |
A⊂B | Proper Subset | Every element in A is in B, and A is smaller than B. |
P(A) | Power Set | All subsets of A |
A=B | Equality | Both A and B have the same elements. |
A-B or A\B | Difference (Relative Complement) | Elements in A which are not in B |
a∈A | Element of | a is in the set A |
a∉A | Not element of | a is not in the set A |
|A| | Cardinality | The number of elements of the set A |
A×B | Cartesian Product | The set of all ordered pairs where the first element is from A, and the second is from B |