Why non-equality check of one variable against many values always returns true?

Question

I have a variable v in my program, and it may take any value from the set of values

\"a\", \"b\", \"c\", ..., \"z\"

A

Answer 1

Use &&/AND/and, not ||/OR/or:

v != "x" && v != "y" && v != "z"

Problem

If an if block is always executed, the condition for the if block always evaluates to true. The logical expression must be wrong.

Let us consider v != "x" || v != "y" || v != "z" for each value of v.

• When v = "x",

  v != "x" becomes "x" != "x", which is false.
  v != "y" becomes "x" != "y", which is true.
  v != "z" becomes "x" != "z", which is true.

  The expression evaluates to false || true || true, which is true.

• When v = "y", the expression becomes

  "y" != "x" || "y" != "y" || "y" != "z"
  

  or true || false || true, which is true.

• When v = "z", the expression becomes

  "z" != "x" || "z" != "y" || "z" != "z"
  

  or true || true || false, which is true.

• For any other value for v, the expression evaluates to true || true || true, which is true.

Alternatively, consider the truth-table:

       │     A          B          C      │
  v    │  v != "x"   v != "y"   v != "z"  │  A || B || C
───────┼──────────────────────────────────┼──────────────
 "x"   │    false      true       true    │     true
 "y"   │    true       false      true    │     true
 "z"   │    true       true       false   │     true
other  │    true       true       true    │     true

As you can see, your logical expression always evaluates to true.

Solution

What you want to do is, find a logical expression that evaluates to true when

(v is not "x")and(v is not "y")and(v is not "z").

The correct construction is,

• for C-like languages (eg. c#, javascript-(may need the strict equality operator !==), php)

  if (v != "x" && v != "y" && v != "z")
  {
      // the statements I want to be executed
      // if v is neither "x", nor "y", nor "z"
  }
  

• for Pascal-like languages plsql

  IF (v != 'x' AND v != 'y' AND v != 'z') THEN
      -- the statements I want to be executed
      -- if v is neither "x", nor "y", nor "z"
  END IF;
  

De Morgan's law

By De Morgan's law, the expression can also be rewritten as (using C-like syntax)

!(v == "x" || v == "y" || v == "z")

meaning

not((v is "x")or(v is "y")or(v is "z")).

This makes the logic a bit more obvious.

Specific languages

Some languages have specific constructs for testing membership in sets, or you can use array/list operations.

• sql: v NOT IN ('x', 'y', 'z')

• javascript: ["x", "y", "z"].indexOf(v) == -1

• python: v not in {"x", "y", "z"}

• java: Arrays.asList("x", "y", "z").contains(v)

• java-9 (and above): Set.of("x", "y", "z").contains(v)