Answer:
Consider,
e be the identity element in I+ with respect to *
a * e = a = e * a, ∀ a ∈ I+
a * e = a and e * a = a, ∀ a ∈ I+
a + e = a and e + a = a, ∀ a ∈ I+
e = 0, ∀ a ∈ I+
Hence, 0 is the identity element in I+ with respect to *.
Find the identity element in the set I+ of all positive integers defined by a * b = a + b for all a, b ∈ I+.
Find the identity element in the set I+ of all positive integers defined by a * b = a + b for all a, b ∈ I+.