Constraints (Meta) Math Example 2

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Example 2

medium
An integer nn satisfies two constraints: n>0n > 0 and n<10n < 10, and also nn is prime. List all valid values of nn.

Solution

  1. 1
    Constraint 1: n∈{1,2,3,4,5,6,7,8,9}n \in \{1, 2, 3, 4, 5, 6, 7, 8, 9\} (positive integers less than 10).
  2. 2
    Constraint 2: nn must be prime. The primes in this set are 2,3,5,72, 3, 5, 7.
  3. 3
    Valid values: n∈{2,3,5,7}n \in \{2, 3, 5, 7\}.

Answer

n∈{2,3,5,7}n \in \{2, 3, 5, 7\}
When multiple constraints apply simultaneously, the solution set is the intersection of all individual constraint sets. Each constraint narrows the possibilities.

About Constraints (Meta)

Constraints are conditions, rules, or boundaries that restrict which values or solutions are allowed in a mathematical problem, narrowing an infinite space of possibilities to a manageable set.

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More Constraints (Meta) Examples

Example 1 easy

Solve [formula] and identify all constraints on [formula] before solving.

Example 3 easy

State the domain constraint for [formula] and solve for [formula] when [formula].

Example 4 medium

A rectangle has area 36 cm² and integer side lengths. List all constraints and find all valid dimens

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