Let U = R. If A = x ∈ R: 0

Question

Let U = R. If A = x ∈ R: 0 < x < 2 B = x ∈ R: 1 < x le 3 which of the following is incorrect? (A) A' = x ∈ R: x le 0 or x ge 2  (B) B' = x ∈ R: x le 1 or x > 3  (C) A ∪ B = x ∈ R: 0 le x le 3  (D) A ∩ B = x ∈ R: 1 < x < 2

Tardigrade Admin · Accepted Answer

A' = R - A = x ∈ R: x le 0 or x ge 2

B' = R - B = x ∈ R: x le 1 or x > 3 A ∪ B = x ∈ R: x ∈ A or x ∈ B = x ∈ R: 0 < x le 3 A ∩ B = x ∈ R: x ∈ A and x ∈ B = x ∈ R: 1 < x < 2

Q. Let $U = R$ . If $A = {x \in R : 0 < x < 2}$ ,
$B = {x \in R : 1 < x \leq 3}$ , which of the following is incorrect?

$A^{'} = {x \in R : x \leq 0$ or $x \geq 2}$

$B^{'} = {x \in R : x \leq 1$ or $x > 3}$

$A \cup B = {x \in R : 0 \leq x \leq 3}$

$A \cap B = {x \in R : 1 < x < 2}$

$A^{'} = R - A = {x \in R : x \leq 0$ or $x \geq 2}$

$B^{'} = R - B = {x \in R : x \leq 1$ or $x > 3}$
$A \cup B = {x \in R : x \in A$ or $x \in B}$
$= {x \in R : 0 < x \leq 3}$
$A \cap B = {x \in R : x \in A$ and $x \in B}$
$= {x \in R : 1 < x < 2}$

Q. Let U=R. If A={x∈R:0<x<2}, B={x∈R:1<x≤3}, which of the following is incorrect?

A′={x∈R:x≤0 or x≥2}

B′={x∈R:x≤1 or x>3}

A∪B={x∈R:0≤x≤3}

A∩B={x∈R:1<x<2}