Operators and Operands

Subsection 2.1.3 Operators and Operands

We won’t get very far if all we have to use are simple statements alone – we need to be able to combine statements to form new, more expressive ones. This is similar to working with numbers: if you have no operations (such as addition and multiplication), you can’t do much.

In logic, statements take the place of numbers. Logical operations will replace arithmetic operations. Otherwise, you will see that the two systems, arithmetic and logic, are very similar.

We shall call the logical operations operators. Examples are not, or, and, and implies (just as \(+ \) ,\(- \) , and \(* \) are arithmetic operators). We shall call statements operands. That just means the objects on which the operators act.

Thus, if we say, “Jim is tall or Joe is short”, there are two operands: “Jim is tall” and “Joe is short”, and there is one operator: or.

If we say, “Jim is not tall”, there is one operand, “Jim is tall”, and there is one operator: not

English Aside
English, in the interest of efficient communication, sometimes lets us shorten sentences so that it’s not completely obvious what the operands are. To find them, we may need to expand sentences into their full constituent parts.

For example, consider the sentence, “Chris likes tacos and guacamole”. There are really two statements here, conjoined with “and”. The two statements (operands) that are lurking here are, “Chris likes tacos” and “Chris likes guacamole”.