Disjunction in Discrete Mathematics


If p and q are two statements, the disjunction of p and q is the compound statement denoted by p ^ q and read as “p or q”. The statement p v q is true if at least one of p or q is true. The candidate must know English or Hindi, certainly would not reject a candidate if he knows both languages). It is false when both p and q are false. The truth of p v q is given in the truth table shown below:

The English word “or” can be used in two different senses – as an inclusive (“and/or”) or exclusive (“either/or”). For example, consider the following statements:

1. p: He will go to Delhi or Calcutta.

2. q: There is something wrong with the bulb or with the circuit.

In the compound statement(1), the disjunction of the statements p has been used in an exclusive sense (p or q but not both) that is to say one or other possibility exists but not both. A person can not do both.

In compound statement(2), the connective is being used in an inclusive sense (p or q or both). In this case at least one of the two possibilities occurred. However both could have occurred, we shall always use ‘or’ in the inclusive sense unless it is started.

Example: Assign a truth value to each of the following statements.
i. 5 < 5 v 5 < 6 ii. 5 x 4 = 21 v 9 + 7 = 17 Solution: i. True, since one of its components viz, 5 < 6 is true. ii. False, since one of its components viz, 6+4 = 10 is true.