Question 1 In each case, verify whether the relation is symmetric, transitive, and whether it is reflexive. In each case also conclude whether the relation is (or is not) an equivalence relation on the respective set. Justify your answer and show all work. (i) The set is Z (the integers) and the relation is {(x,y) : 17 divides (x+y)}. (ii) The set is C (the set of all complex numbers) and the relation is {(x,y) : ||x|| = ||y||}, where ||z|| denotes the complex norm of z. (iii) The set is {a,b,c,d} and the relation is {(a, a), (b, b), (c,c), (d,d), (a,b), (b, a),(a, c), (d, c)}.

Q: The relation on the real numbers R defined by a ~ b if both a > b and b>a is not an equivalence…

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Q: Let R1 = {(a,b) E R²|a > b}, R2 = {(a, b) E R²|a < b} and a) R3 = {(a, b) E R²|a + b} be relations…

A: we have  R1={(a,b)∈R2|a≥b}R2={(a,b)∈R2|a&lt;b}R3={(a,b)∈R2|a≠b}

Q: 1. Let A = {blue, yellow, red}, B = of the relations below (a) determine if it is a function (b) if…

A: R1: D X B={(cat,blue),(cat,red)} So, {(cat,blue)} ⊂{(cat,blue),(cat,red)} Therefore R1 is a…

Q: 2. Let A:= {1,2, 3, 4} =: B and T:= {(a, b) E A x B | l e Z}. (a) Find A x B. (b) Find T (c) Check…

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Q: For each statement determine that if we need a function or binary relation. What are the domain and…

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Q: Let X = {a} and y = {a, b}, do the following. (a). Use the set-roster notation to write set (X x X)…

A: Define a relation which violate the well define ness

Q: Check whether the following relations are reflexive, symmetric, transitive and anti-symmetric and…

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Q: a) Relation R is defined on Z as follows: for every a, b € Z, a R bif 4 | (a - b) (i.e., 4 divides…

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Q: By listing the elements as ordered pairs, define a relation on the set A = {e, 2, 7, ♡} which is:…

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Q: It is based upon properties of relations. *Explanation is mandatory. Check whether the following…

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Q: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

Q: 2. Let A={1, 2, 3, 4, 5, 6} and let R be a relation on A defined as follows: Va,be A, (a,b)…

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Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

A: If R is any symmetric relation on a set A, then R-1 is symmetric.Proof :1. Let R be any symmetric…

Q: Define the relation R over integers as follows: R = { (a, b) | |a - b| < 5 } Determine if R is (a)…

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Q: 11. ( a) b) c) [1 1 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 0 1 1…

A: 11. Consider the relation on A = {1, 2, 3} represented by the matrix 111010011   (a) To determine:…

Q: Q1. Let A be a set of nonzero integers and let be the relation on A defined by (a, b) - (c, d)…

A: Solution:-

Q: Write the relation R = {(x, x3) : x is a prime number less than 10} in roster form.

A: Prime numbers less than 10 are 2,3,5,7

Q: (b) Riley also wants to find the equivalence class of 0 with respect to . Help Riley by giving your…

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Q: Let A={5,10,15,20, 25} and a partition of A be: {5,25},{10, 20} , {15} (a) Write all pairs of the…

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