# Permutations and Combinations

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A.Consider the partial order less than or equal to(<=) on the set X of positive integers given by "is a divsor of." Let a and b be two integers. Let c be the largest integer such that c<=a and c<=b and let d be the smallest integer such that a<=d and b<=d. What are c and d?

b. Prove that the intersection of R and S of two equivalence relations R and S on a set X is also an equivalence relation on X. Is the union of two equivalence relations on X always an equivalence relation?

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Permutations and Combinations are generated. The expert proves that the intersection of R and S on a set on a set X.

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a. Answer:

c is the greated common divisor of a and b. i.e., c = gcd(a, b).

d is the least common multiple of a and b. i.e., d = lcm(a, ...

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