Conjunction in Discrete Mathematics


If p and q are two statements, then the conjunction of p and q is the compound statement denoted by p ^ q and read as “p and q”. The compound statement p ^ q is true when both p and q are true, otherwise, it is false. The truth values of p ^ q are given in the truth table shown below:

Example: Form the conjunction of p and q for each of the following:
i. p: Ram is healthy      q: He has blue eyes

ii. p: It is cold      q: It is raining

i. p ^ q: Ram is healthy and he has blue eyes.

ii. It is cold and raining.

Remarks: The symbol ^ has a specific meaning which is corresponding to the connective and appears in the English language, although and may also be used with some other meanings. In order to the difference, consider the following three statements:
i. Nilima is a girl and Arjun is a boy.

ii. Shekhar switched on the computer and started to work.

iii. Kanchan and Sheela are friends.

In the statement (i) the connectives ‘and’ is used in the same sense as the symbol ^. In (ii) the word ‘and’ is used in the sense of ‘and then’ because the action described in “Shekhar started to work” after the action described in “Shekhar switched on the computer”. Finally, in (iii) the word ‘and’ is not at all a connective.