1. Given that Z denotes the set of all integers and N the set of all natural numbers, describe each of the following sets. a. {x ∈ N | x ≤ 10 and x is divisible by 3} b. {x ∈ Z | x is prime and x is divisible by 2} c. {x ⊆ Z | x2 = 4}

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. Given that Z denotes the set of all integers and N the set of all natural numbers, describe each of the following sets. a. {x ∈ N | x ≤ 10 and x is divisible by 3} b. {x ∈ Z | x is prime and x is divisible by 2} c. {x ⊆ Z | x2 = 4} 2. Let C = {0, 1, 2} and D = {2, 4, 6, 8} and define a relation R from A to B as follows: For all (x, y) ∈ A x B. (x, y) ∈ R means that is an integer. a. Is 1 R 2? Is 2 8? Is (1, 8) ∈ R? Is (2, 6) ∈ R? b. Write R as a set of ordered pairs. c. Write the domain and co-domain of R. Draw an arrow diagram of R. Define a relation A from R to R as follows: For all (x, y) ∈ R x R, (x, y) ∈ A means that x y a. Is 57 A 53? Is (-17) A (-14)? Is (14, 14) ∈ A? Is (-35, 1) ∈ A? b. Draw the graph of A in the Cartesian plane.
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