2. The Four basic vowels

Lojban regards four of these 16 truth functions as fundamental, and assigns them the four vowels A, E, O, and U. These letters do not represent actual cmavo or selma'o, but rather a component vowel from which actual logical-connective cmavo are built up, as explained in the next section. Here are the four vowels, their truth tables, and rough English equivalents:

    A   TTTF    or, and/or
    E   TFFF    and
    O   TFFT    if and only if
    U   TTFF    whether or not

    A   is true if either or both sentences are true;
    E   is true if both sentences are true, but not otherwise;
    O   is true if the sentences are both true or both false;
    U   is true if the first sentence is true, regardless of the truth value of the second sentence.

With the four vowels, the ability to negate either sentence, and the ability to exchange the sentences, as if their order had been reversed, we can create all of the 16 possible truth functions except TTTT and FFFF, which are fairly useless anyway. The following table illustrates how to create each of the 14 remaining truth functions:

    TTTF   A
    TTFT   A with second sentence negated
    TTFF   U
    TFTT   A with first sentence negated
    TFTF   U with sentences exchanged
    TFFT   O
    TFFF   E

    FTTT   A with both sentences negated
    FTTF   O with either first or second negated (not both)
    FTFT   U with sentences exchanged and then second negated
    FTFF   E with second sentence negated
    FFTT   U with first sentence negated
    FFTF   E with first sentence negated
    FFFT   E with both sentences negated