Sr Examen
Expresión ¬(A↔B)↔((A→B)∧(B→A))
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(¬(a⇔b))⇔((a⇒b)∧(b⇒a))
$$\left(\left(a \Rightarrow b\right) \wedge \left(b \Rightarrow a\right)\right) ⇔ a \not\equiv b$$
Solución detallada
$$a ⇔ b = \left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)$$
$$a \not\equiv b = \left(a \wedge \neg b\right) \vee \left(b \wedge \neg a\right)$$
$$a \Rightarrow b = b \vee \neg a$$
$$b \Rightarrow a = a \vee \neg b$$
$$\left(a \Rightarrow b\right) \wedge \left(b \Rightarrow a\right) = \left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)$$
$$\left(\left(a \Rightarrow b\right) \wedge \left(b \Rightarrow a\right)\right) ⇔ a \not\equiv b = \text{False}$$
$$a \not\equiv b = \left(a \wedge \neg b\right) \vee \left(b \wedge \neg a\right)$$
$$a \Rightarrow b = b \vee \neg a$$
$$b \Rightarrow a = a \vee \neg b$$
$$\left(a \Rightarrow b\right) \wedge \left(b \Rightarrow a\right) = \left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)$$
$$\left(\left(a \Rightarrow b\right) \wedge \left(b \Rightarrow a\right)\right) ⇔ a \not\equiv b = \text{False}$$
Tabla de verdad
+---+---+--------+ | a | b | result | +===+===+========+ | 0 | 0 | 0 | +---+---+--------+ | 0 | 1 | 0 | +---+---+--------+ | 1 | 0 | 0 | +---+---+--------+ | 1 | 1 | 0 | +---+---+--------+