Problem 29E

Give a recursive definition of each of these sets of ordered pairs of positive integers. Use structural induction to prove that the recursive definition you found is correct. [Hint: To find a recursive definition, plot the points in the set in the plane and look for patterns.]

a) S = {(a, b) | a ∈ Z+, b∈ Z+, and a + b is even}

b) S = {(a. b) | a ∈ Z+, b ∈ Z+, and a or b is odd }

c) S = ¡(a, b) | a ∈ Z+, b ∈ Z+, a + b is odd and 3 | b}

Explaining Inequality: Marxist Explanation Karl Marx (18181883) What determine who on the top who on the bottom o There are two perspectives: one is Karl Marx, and another is Max Weber that explain. The difference of what is social inequality produce by one single line mechanism or social inequality produce by multiple mechanism. Marx is one that claim the ideal of one single line mechanism that produce all of the social inequality. And Weber complicate of Marx’s idea. Possible that all variety of inequality are perhaps reducible to one single underline mechanism. Marx would never had denied there are not all source of inequality, but he argued that at the bottom one kind of inequality is fundam