Critical Thinking by Example

Chapter 3: Necessary and Sufficient Conditions

Material covered in this chapter 3.1 The meaning of necessary and sufficient conditions 3.2 Conditionals and necessary and sufficient conditions 3.3 The relationship between conditionals and disguised conditionals 3.4 Contrapositive

3.1 The Meaning of Necessary and Sufficient Conditions

‘P is necessary for Q’ is equivalent to ‘P is required for Q’. In other words, for our purposes, necessary = required. ‘P is sufficient for Q’ is equivalent to ‘P is enough for Q’. In other words, for our purposes, sufficient = enough.

Example 3.1: An example of a necessary and a sufficient condition.

Being a bachelor is sufficient for being a male. Being male is necessary for being a bachelor.

Being a bachelor is sufficient for being a male, since being a bachelor is enough to be a male. Being a male is necessary for being a bachelor, since being a male is required for being a bachelor.

2. Conditionals and Necessary and Sufficient Conditions

Conditionals are sentences of this form: If p, then q. In the sentence, ‘If p then q’, ‘p’ is the antecedent and ‘q’ is the consequent. P is sufficient for Q. Q is necessary for P.