Consider the following sentence:

A project is a large and/or complex undertaking.

To me, the expression “and/or” seems redundant since in formal logic “or” implies “and”:

`Table: truth table for Table: truth table for Table: truth table for logical OR (i.e. ∨). logical AND (i.e. ∧). exclusive OR (i.e. ⊕). ----------------------- ----------------------- ----------------------- A B A ∨ B A B A ∧ B A B A ⊕ B ------- ------- ------- ------- ------- ------- ------- ------- ------- F F F F F F F F F F T T F T F F T T T F T T F F T F T T T T T T T T T F ----------------------- ----------------------- -----------------------`

Hence, I simply use “or” in place of “and/or”:

A project is a large or complex undertaking.

To me this implies that a project is:

- Either large.
- Or complex.
- Or both.
Am I correct?

On the other hand, using “either/or” seems to imply exclusive “or”:

A project is either a large or a complex undertaking.

This implies that a project is:

- Either large.
- Or complex.
- But not both.
If using “or” does imply “either/or/both”, then I believe that it’s incorrect to use “and/or” at all. Am I correct in assuming so?

**Answer**

The *or* of English is not equivalent to the *or* of formal logic. In many cases, English *or* actually means the *exclusive or* of logic. For instance, if you say:

Turn left or right at the intersection.

it’s exclusive, because it’s not possible to do both. Or you might ask:

Are you having a boy or a girl?

(Although a logician having fraternal twins might humorously answer “yes”.)

As a result, the phrase *and/or* is used to make it clear that the inclusive sense is intended.

However, there are many contexts where it’s clear that only the inclusive meaning makes sense. In this case, you can simply say *or* and be understood. Your example sentence is such a case — no one would assume that *large* and *complex* are mutually exclusive (in fact, one often implies the other). Another example is:

He can’t read or write.

This last sentence also obeys de Morgan’s Law, as it means the same thing as

He can’t read and he can’t write.

**Attribution***Source : Link , Question Author : Aadit M Shah , Answer Author : Barmar*