Question

The -1 is an negative exponent 2. Let m : N × N → N be defined

by m({a, b}) = a · b. (a) Find m−1(1).

Answer 1

The function m({a, b}) = a · b represents a binary operation called multiplication on the set of positive integers. To find m^-1(1), we need to determine the pairs of positive integers {a, b} such that a · b equals 1. The only pair that satisfies m({a, b}) = a · b = 1 is {1, 1}. Therefore, m^-1(1) = {1, 1}.

Step-by-step explanation:

The function m({a, b}) = a · b represents a binary operation called multiplication on the set of positive integers. To find m⁻¹(1), we need to determine the pairs of positive integers {a, b} such that a · b equals 1.

Since 1 can only be obtained by multiplying 1 with itself (1 · 1 = 1), the only pair that satisfies m({a, b}) = a · b = 1 is {1, 1}.

Therefore, m⁻¹(1) = {1, 1}.