在韦恩图上,给表示 A′∪BA' \cup B 的区域涂上阴影。 用集合符号描述阴影区域。

先不看答案,让 AI 诊断你卡在哪里?

它不会直接告诉你答案,而是问你卡在哪一步看看 AI 是怎么陪你一步步弄懂这道题的

完整解法

5(a)

1. Identify the regions included in $A' \cup B$ and shade them

A′A' is the region outside AA.

A′∪BA' \cup B means all points that are in A′A' or in BB.

So shade:

  • all regions outside circle AA,
  • the whole of circle BB, including A∩BA \cap B.

The only region not shaded is A∩B′A \cap B', the part inside AA but outside BB.

答案

Shade all regions outside circle AA, and shade the whole of circle BB including the overlap A∩BA \cap B. Leave unshaded only the part of AA that is not in BB.

5(b)

1. Describe the shaded annular region in set notation

The shaded region is inside AA and outside BB.

Hence the region is
A∩B′A \cap B'.

答案

A∩B′A \cap B'

AI 分析,可能出错

用 AI 批改,圈出写错的那一步,并自动将你的薄弱点存入错题本,形成你的错因库。

同一知识点的其他题

  1. 1已知 ξ={x:x is polygon},\xi = \{x: x \text{ is polygon}\}, p={x:x is a parallelogram},p = \{x: x \text{ is a parallelogram}\}, q={x:x is a quadrilateral},q = \{x: x \text{ is a quadrilateral}\},…
  2. 2ξ={integers x:2<x≤12}\xi = \{\text{integers } x: 2 < x \le 12\} A={prime numbers}A = \{\text{prime numbers}\} B={factors of 12}B = \{\text{factors of 12}\} C={greater than 100}C = \{\text{greater than } \sqrt{100}\}…
  3. 3在答题区给出的韦恩图中,用阴影表示集合 A∩B′A \cap B'。 ε=x:x is an integer and 1≤x≤100ε = {x: x \text{ is an integer and } 1 \le x \le 100} P=x:x is a perfect squareP = {x: x \text{ is a perfect square}}…
  4. 4三年级(2)班有56名学生,这个月进行了两次数学测试:第一次得100分的学生的学号是6,9,15,16,27,33,56;第二次得100分的学生的学号是:7,9,16,27,36,40,48,51,53。 1.第一次得100分的有( )人。…
  5. 5ε={integer x:0<x≤12}\varepsilon = \{\text{integer } x : 0 < x \le 12\} A={prime numbers}A = \{\text{prime numbers}\} B={numbers that have at least 2 distinct factors}B = \{\text{numbers that have at least 2 distinct factors}\}…