Exercise 2-103

Write the 2x2 identity matrices for each of the quantales:

  1. \((\mathbb{N},\leq,1,*)\)

  2. \(\mathbf{Bool}:=(\mathbb{B},\leq,true,\land)\)

  3. \(\mathbf{Cost}:=([0,\infty],\leq,0,+)\)

Solution(1)
  1. 1 0
    0 1
  2. T F
    F T
  3. 0 \(\infty\)
    \(\infty\) 0