Question

2. Sabendo que A=5, B=4 e C=3 e D=6, informe se as expressões abaixo são verdadeiras ou falsas. Explique seu raciocínio no uso dos OPERADORES LÓGICOS de acordo com a tabela a seguir:

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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⠀⠀☞ De acordo com uma tabela verdade para duas proposições temos que os três enunciados são verdadeiros. ✅

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⠀⠀ Vamos inicialmente registrar o significado de alguns conectivos lógicos e uma tabela verdade para duas proposições p e q:

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

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

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

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$\LARGE\blue{\sf V~\cap~V}$

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$\LARGE\blue{\sf V}$ ✅

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

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$\LARGE\blue{\sf  (5 + 4 > 10)~\cup~(5 + 4) = (3 + 6)}$

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$\LARGE\blue{\sf \overbrace{\small (9 > 10)}^{F}~\cup~\overbrace{\small (9 = 9)}^{V}}$

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$\LARGE\blue{\sf F~\cup~V}$

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$\LARGE\blue{\sf V}$ ✅

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

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

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$\LARGE\blue{\sf V~\cap~V}$

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$\LARGE\blue{\sf V}$ ✅

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

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

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