The word \"or,\" expressed by the logical term \"disjunction,\" has two, distinc
ID: 3487974 • Letter: T
Question
The word "or," expressed by the logical term "disjunction," has two, distinctively different, meanings. One is the "exclusive disjunction" ("strong or"), which is true when EXACTLY one of the disjoints is true, and false when they are both false and both true. The other is the "inclusive disjunction" ("weak or"), which is true when AT LEAST one of the disjoints is true and false only when they are both false. The difference is in the case when both disjoints are true: in that case, the exclusive disjunction is false and the inclusive disjunction is true. (You could say that the inclusive disjunction is more like "and/or.")
The logical connective "disjunction" is the INCLUSIVE disjunction. Its truth table is:
A
B
A v B
T
T
T
T
F
T
F
T
T
F
F
F
Write a "formula" which will express the exclusive disjunction using any combination of the connectives you know - conjunction, negation, and (inclusive) disjunction. In other words, write a formula in statement logic which says something like "A or B
A
B
A v B
T
T
T
T
F
T
F
T
T
F
F
F
Explanation / Answer
Disjunctive Syllogism is symbolised be"or" "v" (wedge)
The disjunctive function has commutative, associative as well as idempotent properties that are shown as following:
Example
A=you take the apple
B= you take the orange
(A v( B v C))
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