Question

Define by using the set-builder notation by using the condition as predicate logic.

We can only use these operations + and *

1) Nonnegative numbers that are divisors of 42.

2) The set pairs of consecutive integers that are even. For example (24, 26) or (30, 28) - These pairs would hold.

What I have is this:

1. {x | x * y = 42, x,y ∈ N} or   {x | (x,y) ∈ N*N and x*y = 42}

2.   { (2x,2y) | y = x+2 or x = y+2, x,y ∈ Z }

Please give me your opinion or offer another better solution. Thank you!

Answer 1

Ans. Yes, your solution is absolutely correct but for Part 2 I am suggesting a better solution. Now, I am going to explain step-by-step how these solutions can be achieved. Now, I am attaching solution as under:

1: Non- negative numbers that are divisors of 42. Divisons of 42 in a set, say A where, - A = {1, 2, 3, 6, 7, 14, 21, 429 and this A EN. (N=natural no.). So, we form new set B where x, y El and xy = 42 In pet builder form, B =colc, y): x*y = 42, #aceye A } ORI B = {x:(0.4) ENN and 2*Y-4231 OR B = { x: xy = 42, tx., 4 ENIE 2. The set pains of consecutive integers are even Set of integers I = {0,+1,£2, 53,.... 2 So det of pair of consecutive even integers Say A ¢ (0,2), (2,4),(4,6), (2,0) 0(-4,-2. (26,24), (30, 20)...} and so on for such type of set;

in set-builder notation, we may write A=:( 200 , 2x2+2), xEZ}] suppose we take a = 0, 1, 2, 3 ... respectively we get required set as A = {(2x0, 2x0+2), (1x2, 2x1+2), (2x3, 2x3+2), and so on. A = {0,2), (2,4), (620), ---