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krek1111 [17]
3 years ago
6

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 an

d 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.

Mathematics
1 answer:
Elza [17]3 years ago
4 0

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\}.

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