# Logical Operations

The basic logical operations are not, or, and. These operations are used to combine two or more propositions to form compound propositions.

Not (Negation):

If p is a proposition then, negation of p is defined as the opposite of p. In simple words we can say that if p is true then negation of p is false and vice versa. It is denoted as ~p.

For example, p=20 is a multiple of 3, then ~p=20 is not a multiple of 3.

And (Conjunction):

If p and q are two propositions then, conjunction of p and q is a compound proposition which is true only when both p and q are true and false for the rest of the cases. It is denoted as p^q.

For example, p=Today is Sunday. q=Today is holiday, then p^q=Today is Sunday and today is holiday.

Or (Dis-junction):

If p and q are two propositions then, dis-junction of p and q is a compound proposition which is false only when both p and q are false and true for the rest of the cases. It is denoted as pvq.

For example, p=It is raining. q=The road is wet, then pvq=It is raining or the road is wet.