Question

True/False: Negative numbers closed under subtraction. Provide an example if false

Answer 1

Consider a set M, and an operation *.

Let a and b be in M, then M is closed under operation * if :

a*b, and b*a produce an element of M
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The set of negative numbers (set M) is not closed under subtraction (the operation *).

Consider 2 numbers a=-9 and b=-6 which certainly are in M.

-9*(-6) = -9-(-6)=-9+6=-3 ∈ M (note that * is the regular subtraction -)

(-6)*(-9)=-6-(-9)=-6+9=3 ∉ M