Question

sabendo que A=5, B=4, C=3 e D=6, informe se as expressões abaixo são verdadeiras ou falsas
a) (A > C) AND (C <= D) ( )
b) (A+B) > 10 OR (A+B) = (C+D) ( )
c) (A >= C) AND (D >= C) ( )

Answer 1

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⠀⠀☞ As 3 expressões são verdadeiras. ✅

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➡️⠀Inicialmente lembremos o que cada conectivo lógico representa:

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$\red{\boxed{\pink{\boxed{\begin{array}{rlclr}&&&&\\&\orange{\sf p \cup q}&\pink{\Longrightarrow}&\orange{\sf p~ou~q}&\\&&&&\\&\orange{\sf p \cap q}&\pink{\Longrightarrow}&\orange{\sf p~e~q}&\\&&&&\\&\orange{\sf p \rightarrow q}&\pink{\Longrightarrow}&\orange{\sf se~p~ent\tilde{a}o~q}&\\&&&&\\&\orange{\sf p \iff q}&\pink{\Longrightarrow}&\orange{\sf p~se,~e~somente~se,~q}&\\&&&&\\&\orange{\sf \tilde{}~p}&\pink{\Longrightarrow}&\orange{\sf n\tilde{a}o~p}&\\&&&&\\\end{array}}}}}$

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➡️⠀Vamos também registrar nossa tabela verdade padrão:

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$\red{\boxed{\pink{\boxed{\orange{\begin{array}{c|c|c|c|c|c}&&&&&\\\sf ~p~~&\sf ~~q~~&\sf p \cup q&\sf p \cap q&\sf p \rightarrow q&\sf p \iff q\\&&&&&\\\sf V&\sf V&\sf V&\sf V&\sf V&\sf V\\&&&&&\\\sf V&\sf F&\sf V&\sf F&\sf F&\sf F\\&&&&&\\\sf F&\sf V&\sf V&\sf F&\sf V&\sf F\\&&&&&\\\sf F&\sf F&\sf F&\sf F&\sf V&\sf V\\&&&&&\\\end{array}}}}}}$

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a) (A > C) AND (C <= D)

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$\LARGE\blue{\sf \overbrace{(5 > 3)}^{V}~e~\overbrace{(3 \leq 6)}^{V}}$

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$\LARGE\blue{\sf V~\cap~V = V}$  

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$\huge\green{\boxed{\rm~~~\red{A)}~\blue{(V)}~~~}}$ ✅

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b) (A+B) > 10 OR (A+B) = (C+D)

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$\large\blue{\sf \overbrace{(5 + 4) > 10}^{F}~ou~\overbrace{(5 + 4) = (3 + 6)}^{V}}$

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$\LARGE\blue{\sf F~\cup~V = V}$  

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$\huge\green{\boxed{\rm~~~\red{B)}~\blue{(V)}~~~}}$ ✅

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c) (A >= C) AND (D >= C)

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$\LARGE\blue{\sf \overbrace{(5 \geq 3)}^{V}~e~\overbrace{(6 \geq 3)}^{V}}$

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$\LARGE\blue{\sf V~\cap~V = V}$  

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$\huge\green{\boxed{\rm~~~\red{C)}~\blue{(V)}~~~}}$ ✅

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

⠀⠀☀️ Leia mais sobre conectivos lógicos e valor verdade:

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✈ https://brainly.com.br/tarefa/38427225

✈ https://brainly.com.br/tarefa/38427212

✈ https://brainly.com.br/tarefa/38427233

✈ https://brainly.com.br/tarefa/38348117

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⠀⠀⠀⠀⠀☕ $\Large\blue{\text{\bf Bons~estudos.}}$

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($\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }\LaTeX}$✍

❄☃ $\sf(\purple{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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$\Huge\green{\text{ \underline{\red{\mathbb{S}}\blue{\mathfrak{oli}}~}~\underline{\red{\mathbb{D}}\blue{\mathfrak{eo}}~}~\underline{\red{\mathbb{G}}\blue{\mathfrak{loria}}~} }}$ ✞

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