Exclusive disjunction (exclusive “or”, strict disjunction, symmetric difference)

Exclusive disjunction is designated as AÅ B or A Δ B or A+B (rarely).

It is read as “or A or B”, “A plus B“.

A	B	Or A or B
T	T	F
T	F	T
F	T	T
F	F	F

Other spartanic women, entrusting a shield to the son, has said laconic: «With it or on it».

The woman differently used such proposition, saying the famous aphorism. Her composite proposition is true only in two cases: then, when first of the partial propositions included in it («with a shield») is true, and second is false («on a shield»), or then, when the first proposition is true and second is false.

In similar cases speak, that the union «OR» has separating sense and expresses a so-called strict disjunction.

Other example is: “I will study medicine either in Poltava or in Sankt-Peterburg next year”. As you can’t be in two places in one time, this phrase is strict disjunction.

Equivalention (is necessary and enough) (equivalence, identity)

A logic operation named «when and in only case when» (versions: «it is necessary and enough», «if and only if»).

The composite proposition derived from two initial with the help of this operation, is named them equivalention; as this operation is named also.

Equivalention of two propositions is true in only case when, when either both propositions are true or both are false, that is the truth values that and other coincides.

A	B	A if and only if B
T	T	T
T	F	F
F	T	F
F	F	T

A logic operation named «when and in only case when» (versions: «it is necessary and enough», «if and only if»).

The composite proposition derived from two initial with the help of this operation, is named them equivalention; as this operation is named also.

Equivalention of two propositions is true in only case when, when either both propositions are true or both propositions are false, that is the truth values that and other coincide.

Implication is designated as: A~B or A ≡ B or A↔B or A B.

It is read as “A then and only then, when B” or “A is equivalent to B”.

Equivalence A↔B we can write as combination of implications: AàB ^ BàA.

Nonconjunction (Sheffer function, stroke function)

Sheffer-stroke operation, NAND operation, NOT-AND operation.

It is designated as: A | B

It is mean that result is true, if false both A and B.

A	B	false that A and B
T	T	F
T	F	T
F	T	T
F	F	T

Example: “I will study medicine next year if and only if I will pass all entrance examinations”.