Discrete Mathematics

Question

A.     Consider the following set:

 E = {x | x is an integer less than 12}

Write S if the following sets are subset of E and write such relation using the subset notation. Write D if the following sets are disjoint to E.

a.        F = { -1, -354, 0, 1, 2}

b.       C = { -100.13, 12, 100, 0.17}

c.       G= {114, 13, 100}

d.       A = {11}

e.       D = {20, 21, 22….}

Answer 1

E is the set of all integers that are strictly less than 12.

Notice that the sets C and G are finite sets and have largest elements 100 and 114 respectively. Hence, those are clearly not subsets of E. The set D is an infinite set who's smallest element is 20, so D is not a subset of E either.

A is clearly a subset of E. The largest element of F is 2, so F is a subset of E as well.

Therefore:

1. F ⊆ E
2. C ⊄ E
3. G ⊄ E
4. A ⊆ E
5. D ⊄ E