Maths Olympiad Prep

Library / /157 of 520

Algebra Difficulty 3.0 Junior Find the answer

If set A={xx<2}A=\{x | x < 2\}, B={x1<x<7}B=\{x | 1 < x < 7\}, then AB=A\cup B=

Pick one

Solution

To solve this problem, let's analyze the sets AA and BB and their union step by step.

1. **Understanding Set AA:** The set AA is defined as A={xx<2}A=\{x | x < 2\}. This means AA includes all real numbers that are less than 2.

2. **Understanding Set BB:** The set BB is defined as B={x1<x<7}B=\{x | 1 < x < 7\}. This means BB includes all real numbers that are greater than 1 and less than 7.

3. **Finding the Union ABA\cup B:** The union of sets AA and BB, denoted as ABA\cup B, includes all elements that are in AA, in BB, or in both. Given the definitions of AA and BB, the union will include:
- All numbers less than 2 (from AA)
- All numbers greater than 1 and less than 7 (from BB)

Combining these, we see that ABA\cup B includes all numbers less than 7, since it encompasses both the range of AA and the range of BB. Therefore, we can express the union as AB={xx<7}A\cup B=\{x | x < 7\}.

Hence, the correct answer is A\boxed{A}.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.