The word “And”

The connective "And" joins two or more component statements into one, and it has a simple, strict rule for truth:

1. A compound statement joined by "And" is true only when every one of its component statements is true.
2. It is false if even a single component statement is false — it does not matter whether one, several, or all of the parts fail; one failure is enough to sink the whole compound statement.

For example, p: "42 is divisible by 5, 6 and 7" breaks into three components — "42 is divisible by 5" (false), "by 6" (true), "by 7" (true). Since one component is false, the whole compound statement p is false, regardless of the other two being true. …