Question

If R is the set of all integers with absolute value less than 10, A is its subset containing all natural numbers less than 10 and B is the set of all integer solutions of inequality 2x+5<9 that are less than 10 by absolute value (and therefore, it is also a subset of R), draw Venn diagram showing these sets. List elements of sets A, B, their union, and their intersection.

Answer 1

Answer:

See explanation

Step-by-step explanation:

1. R is the set of all integers with absolute value less than 10, thus

$R=\{a\in \mathbb{Z}\ :\ |a|$

2. A is its subset containing all natural numbers less than 10, thus

$A\subset R\\ \\A=\{b\in \mathbb{N}\ :\ b$

3. B is the set of all integer solutions of inequality 2x+5<9 that are less than 10 by absolute value (and therefore, it is also a subset of R). First, solve the inequality:

$2x+5$

Thus,

$B\subset R\\ \\B=\{c\in \mathbb{Z}\ :\ 2c+5$

See the diagram in attached diagram.

Note that

$A\cup B=R\\ \\A\cap B=\{1\}.$