Logic Symbols

⇁, ~

Negation (not) | A not B

∧, &, ・

Conjunction (and) | A and B

∨

Inclusive disjunction (or) | Equivalent to and/or | A and/or B

⊕, ⊻

Exclusive disjunction (xor) | Either A or B, but NOT both

|, ↑

Alternative denial (nand) | Means “not both”. | Not A and B (or anything BUT A and B)

↓

Joint denial (nor) | Means neither/nor | A nor B

→, ⊃

Conditional (if/then) | (can be inverted) | If A, then B

⇸

Non-conditional | (can be inverted) | Not if A, then B

⇔, ≡

Biconditional (iff) | Means if and ONLY if. | A, if and only if B [is present]

⇎

Non-biconditional | Not if only if | Not “A if and only if B [is present]”