Definition 1. If A and B are sets, then their symmetric difference is defined to be AAB (AB) U (BA) i.e. AB is the set of elements which lie in exactly one of the sets A or B. Exercise 2. Let be the relation on P(N) defined by AB AB and min(AAB) = A. (i) Prove that is a linear ordering of P(N). (ii) Prove that is not a well-ordering of P(N). Exercise 3. Prove that if m, n Ew satisfy m < n, then there exists pЄ w such that nm+p+. (Hint: Argue by induction on n.)

Q: Given a relation, R on A = {a, b, c, d} on as follows: R = {(а, а), (а, b), (а, d), (b, b), (b, с),…

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Q: 5. Let R be the relation on the set {1, 2, 3, 4, 5} containing the ordered pairs (1, 1), (1, 2), (1,…

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Q: The R is the relation from {1, 2, 3} to {1, 2, 3, 4} with R = {(1, 1), (1, 2), (2, 3), (3, 4), (3,…

A: Here,  R=1,1,1,2,2,3,3,4S=1,0,2,1,3,2,3,0,4,1

Q: Q-3: a) Let R be a relation on A = {1,2,3,4} such that aRb means |ab| ≤ 1. Find the matrix…

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Q: How many symmetric relations on the set A = {1,2, 3, 4, 5, 6, 7, 8} contain the ordered pairs (2,…

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Q: 1. (1 pints) Let A = {a,b,..., z} and B = {1,2,..., 10} and define f = {(c, 6), (b, 9), (b, 8), (d,…

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Q: a ) Let R be the relation on the set A={1,2,3,4} defined by aRb if and only if 2a>b+1. Find the…

A: let A={1,2,3,4}   aRb iff 2a&gt;b+1   first we will find R…