Question

discrete mathematics help

1.

List the order pairs in the relation R from A ={0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a, b) Î R if and only if

a) a = b

b) a + b = 4

c) a > b

d) a|b

//6th edition ((a), (b), (c), and (d) of Exercise 1, Page 527.)

2.

a)

List all the ordered pairs in the relation R = {(a, b) |a divides b} on the set

{1, 2, 3, 4, 5, 6}.

c)

Display this relation in tabular form, as was done in Example 4 on Page 575.

//6th edition ((a) and (c) of Exercise 2, Page 527.)

3.

Determine whether the relation R on the set of all people if reflexive, symmetric, and /or transitive, where (a, b) Î if and only if

a) a is taller b

b) a and b were born on the same day

c) a has the same first name as b

d) a and b have a common grandparent

//(Ignore the question for determining if the relations are antisymmetric.)

//6th edition (Exercise 4, Page 527.)

4.

Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of an equivalence relation that others lack.

a) {(0, 0), (1, 1), (2, 2), (3, 3)}

b) {(0, 0), (0, 2), (2, 0), (2, 2), (2, 3), (3, 2), (3, 3)}

c) {(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)}

// 6th edition ((a), (b), and (c) of Exercise 1, Page 562 and Page 563.)

5.

Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that others lack?

a){(a, b) | a and b are the same age }

b){(a, b) | a and b have the same parents}

e){(a, b) | a and b speak common language}

/6th edition ((a), (b), and (e) of Exercise 2, Page 563.)

6.

Find the equivalent classes of the equivalent relations (a) and (c) of Exercise 1, Page 615.

a) {(0, 0), (1, 1), (2, 2), (3, 3)}

c) {(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)}

7.

Which of these collections of subset are partitions of {1, 2, 3, 4, 5, 6}?

a) {1, 2}, {2, 3, 4}, {4, 5, 6}

b) {1}, {2, 3, 6}, {4}, {5}

c) {2, 4, 6}, {1, 3, 5}

d) {1, 4, 5}, {2, 6}

//6th edition (Exercise 41, Page 564.)

8.

Which of these collections of subsets are partitions of the set of integers?

a) the set of even integers and the set of odd integers

b) the set of positive integers and the set of negative integers

//6th edition ((a) and (b) of Exercise 44, Page 564.)

9.

List the ordered pairs in the equivalence relations produced by these partitions of

{a, b, c, d, e, f, g}.

a) {a, b},{c, d},{e, f, g}

d) (a, c, e, g}, {b, d},{f}

//6th edition ((a) and (d) of Exercise 48, Page 565.)

Answer 1

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