Question

Com resolução por favor !!

Answer 1

Considere os seguintes conjuntos:

$\text{A}=\{\text{pessoas~que~responderam~sim~na~primeira~pergunta}\}$

$\text{B}=\{\text{pessoas~que~responderam~sim~na~segunda~pergunta}\}$

$\text{A}=\{\text{pessoas~que~responderam~sim~na~terceira~pergunta}\}$

Vamos utilizar a seguinte fórmula:

$\text{N}(\text{A}\cup\text{B}\cup\text{C})=\text{N}(\text{A})+\text{N}(\text{B})+\text{N}(\text{C})-\text{N}(\text{A}\cap\text{B})-\text{N}(\text{A}\cap\text{C})-\text{N}(\text{B}\cap\text{C})+\text{N}(\text{A}\cap\text{B}\cap\text{C})$

Pelo enunciado:

$\text{N}(\text{A})=62~~~~~~~~~~~~~~~~~~~~~\text{N}(\text{A}\cap\text{B})=32$
$\text{N}(\text{B})=48~~~~~~~~~~~~~~~~~~~~~\text{N}(\text{A}\cap\text{C})=35$
$\text{N}(\text{C})=45~~~~~~~~~~~~~~~~~~~~~\text{N}(\text{B}\cap\text{C})=22$

E $\text{N}(\text{A}\cup\text{B}\cup\text{C})=88$

Substituindo na fórmula, obtemos:

$62+48+45-32-35-22+\text{N}(\text{A}\cap\text{B}\cap\text{C})=88$

$66+\text{N}(\text{A}\cap\text{B}\cap\text{C})=88$

$\text{N}(\text{A}\cap\text{B}\cap\text{C})=88-66$

$\text{N}(\text{A}\cap\text{B}\cap\text{C})=22$

Logo, $22$ pessoas responderam "sim" às três perguntas.