====== سوال ۱۹ ======

کدام یک از عبارات منطقی زیر معادل با عبارت
‎$\small(B \wedge \sim D) \vee (\sim C \wedge D)$‎ است؟

  - $\small(B \vee \sim C) \wedge (\sim D \vee D)$‎
  - ‎$\small(B \vee \sim D) \wedge (C \vee D)$‎
  - ‎$\small(B \vee D) \wedge (\sim C \vee \sim D)$‎
  - ‎$\small(B \vee \sim D) \wedge (\sim C \vee D)$‎
  - $\small(B \vee D) \wedge (C \vee \sim D)$‎

<پاسخ>
گزینه (۳) درست است.

<WRAP :en>

$(B\wedge \sim D) \vee (\sim C \wedge D) \\ \equiv [B \vee (\sim C \wedge D)] \wedge [\sim D \vee ( \sim C \wedge D)] \\ \equiv [(B \vee \sim C) \wedge (B \vee D) \wedge ( \sim D \vee \sim C) \wedge (\sim D \vee D)] \\ \equiv (B \vee \sim C) \wedge (\sim D \vee \sim C) \wedge (B \vee D) \\ \equiv [ \sim C \vee ( B \wedge \sim D)] \wedge (B \vee D) \\ \equiv [\sim C \wedge (B \vee D)] \vee [( B \wedge \sim D) \wedge (B \vee D)] \\ \equiv [\sim C \wedge (B \vee D)] \vee [(\sim D \wedge B \wedge (B \vee D)] \\ \equiv [\sim C \wedge (B \vee D)] \vee [(\sim D \wedge B) \vee F \\ \equiv [\sim C \wedge (B \vee D)] \vee [(\sim D \wedge B) \vee (\sim D \wedge D)] \\ \equiv [\sim C \wedge (B \vee D)] \vee [\sim D \wedge (B \vee D)] \\ \equiv \small(B \vee D) \wedge (\sim C \vee \sim D)$
</WRAP>
</پاسخ>
  * [[سوال ۲۰|سوال بعد]]
  * [[سوال ۱۸|سوال قبل]]