9. Sınıf Mantık Akıllı Test

9. Sınıf – Mantık (De Morgan)

Adı Soyadı:

Sınıfı:

No:

Tarih / Puan:

1) Aşağıdaki ifade hangisine eşdeğerdir?
\(\left(\left(q \land \left(r' \lor q\right)\right)\right)^{\prime}\)

A) \(\left(\left(\left(q' \lor p'\right) \land \left(q \lor r\right)\right) \lor \left(p' \lor \left(q' \Rightarrow p'\right)\right)\right)\) B) \(\left(\left(\left(r' \land r'\right)\right)^{\prime} \Rightarrow \left(p \land \left(p \land r'\right)\right)\right)\) C) \(\left(\left(q' \lor \left(q \lor r'\right)\right) \Leftrightarrow \left(\left(q \Leftrightarrow p'\right) \Rightarrow q\right)\right)\) D) \(\left(q' \lor \left(r \land q'\right)\right)\) E) \(\left(\left(r' \lor r\right) \land \left(p \Leftrightarrow r'\right)\right)\)

2) Aşağıdaki ifade hangisine eşdeğerdir?
\(\left(\left(r \lor q\right)\right)^{\prime}\)

A) \(\left(\left(p \Leftrightarrow r'\right) \land \left(r' \Rightarrow p\right)\right)\) B) \(\left(\left(q \land p\right) \lor \left(r \Leftrightarrow q'\right)\right)\) C) \(\left(r' \land q'\right)\) D) \(\left(\left(\left(q' \Rightarrow q\right) \land \left(r \land p\right)\right) \oplus \left(\left(r' \lor p'\right) \lor \left(p \Leftrightarrow q'\right)\right)\right)\) E) \(\left(\left(\left(r' \Leftrightarrow r'\right) \Rightarrow \left(r \lor r\right)\right) \oplus \left(\left(p' \land p\right) \lor q\right)\right)\)

3) p, q ve r önermeleri için p = Yanlış, q = Doğru, r = Doğru iken, aşağıdaki ifadelerden hangisi doğrudur?

A) \(\left(p \land \left(q \lor r\right)\right)\) B) \(\left(p \lor q\right)\) C) \(\left(p \land q\right)\) D) \(\left(\left(p \lor q\right)\right)^{\prime}\) E) \(\left(p \Leftrightarrow q\right)\)

4) p, q ve r önermeleri için p = Yanlış, q = Yanlış, r = Yanlış iken, aşağıdaki ifadelerden hangisi doğrudur?

A) \(\left(p \lor \left(q \land r\right)\right)\) B) \(\left(\left(p \land q\right) \Rightarrow r\right)\) C) \(\left(p \land \left(q \lor r\right)\right)\) D) \(\left(q' \land r\right)\) E) \(\left(p \lor q\right)\)

5) Aşağıdaki ifade hangisine eşdeğerdir?
\(\left(\left(p \land q'\right)\right)^{\prime}\)

A) \(\left(\left(\left(p' \land r'\right) \lor \left(r \land r\right)\right) \Leftrightarrow \left(\left(p' \oplus q'\right) \Rightarrow \left(q \Rightarrow r\right)\right)\right)\) B) \(\left(\left(\left(r' \lor q'\right) \oplus \left(r' \land r'\right)\right) \land \left(p' \oplus \left(p \Rightarrow r'\right)\right)\right)\) C) \(\left(p' \lor q\right)\) D) \(\left(r' \Leftrightarrow \left(p' \lor p'\right)\right)\) E) \(\left(\left(q' \lor \left(q \lor q\right)\right) \lor \left(\left(q \land q\right) \Leftrightarrow \left(r' \Rightarrow r'\right)\right)\right)\)

6) Aşağıdaki ifade hangisine eşdeğerdir?
\(\left(\left(\left(r \land q'\right) \land r'\right)\right)^{\prime}\)

A) \(\left(\left(\left(p \lor q\right) \Leftrightarrow \left(p' \oplus p'\right)\right) \Rightarrow \left(\left(r' \Leftrightarrow q'\right) \land \left(p' \lor q\right)\right)\right)\) B) \(\left(r' \lor \left(r' \lor q\right)\right)\) C) \(\left(\left(r' \lor q\right) \lor r\right)\) D) \(\left(\left(\left(r \land q'\right) \Leftrightarrow \left(p' \lor q\right)\right) \land \left(\left(p' \oplus r\right) \oplus \left(q \land q'\right)\right)\right)\) E) \(\left(\left(\left(r' \oplus q'\right)\right)^{\prime} \lor \left(\left(r' \Rightarrow p\right) \oplus \left(q' \oplus q'\right)\right)\right)\)

7) p, q ve r önermeleri için p = Doğru, q = Yanlış, r = Yanlış iken, aşağıdaki ifadelerden hangisi doğrudur?

A) \(\left(p \Leftrightarrow q\right)\) B) \(\left(p \oplus q\right)\) C) \(\left(\left(p \lor q\right)\right)^{\prime}\) D) \(\left(p \land q\right)\) E) \(\left(p \Rightarrow q\right)\)

8) p, q ve r önermeleri için p = Yanlış, q = Doğru, r = Yanlış iken, aşağıdaki ifadelerden hangisi doğrudur?

A) \(\left(\left(p \lor q\right)\right)^{\prime}\) B) \(\left(p' \lor r\right)\) C) \(\left(p \lor \left(q \land r\right)\right)\) D) \(\left(q' \land r\right)\) E) \(\left(p \land \left(q \lor r\right)\right)\)

9) Aşağıdaki ifade hangisine eşdeğerdir?
\(\left(\left(\left(r' \land q'\right) \land r\right)\right)^{\prime}\)

A) \(\left(\left(\left(q' \land r\right) \oplus \left(q \lor p'\right)\right) \land \left(\left(p' \Leftrightarrow p\right)\right)^{\prime}\right)\) B) \(\left(\left(r \lor q\right) \lor r'\right)\) C) \(\left(\left(\left(p \oplus p\right) \lor \left(p \land r\right)\right) \oplus \left(\left(r' \Leftrightarrow p'\right)\right)^{\prime}\right)\) D) \(\left(\left(\left(q' \land r'\right) \lor \left(r \lor r\right)\right) \oplus \left(\left(r \Rightarrow r\right)\right)^{\prime}\right)\) E) \(\left(\left(\left(p \oplus p'\right)\right)^{\prime} \lor \left(\left(p \Leftrightarrow r\right)\right)^{\prime}\right)\)

10) p, q ve r önermeleri için p = Yanlış, q = Yanlış, r = Yanlış iken, aşağıdaki ifadelerden hangisi doğrudur?

A) \(\left(p \lor q\right)\) B) \(\left(p \land \left(q \lor r\right)\right)\) C) \(\left(q' \land r\right)\) D) \(\left(p \lor \left(q \land r\right)\right)\) E) \(\left(p' \lor r\right)\)

11) Aşağıdaki ifade hangisine eşdeğerdir?
\(\left(\left(\left(q \land q\right) \land r\right)\right)^{\prime}\)

A) \(\left(\left(p' \Rightarrow p'\right) \land \left(p \Leftrightarrow r'\right)\right)\) B) \(\left(\left(q' \lor q'\right) \lor r'\right)\) C) \(\left(\left(\left(p' \land r'\right) \Rightarrow \left(q \lor q\right)\right) \lor \left(\left(p \land r\right) \land \left(q' \oplus q'\right)\right)\right)\) D) \(\left(\left(\left(q' \land q'\right) \oplus q'\right) \land \left(\left(r \land q\right)\right)^{\prime}\right)\) E) \(\left(\left(\left(r \land p'\right)\right)^{\prime} \lor \left(\left(r \land r\right) \land \left(p' \land r'\right)\right)\right)\)

12) p, q ve r önermeleri için p = Yanlış, q = Doğru, r = Doğru iken, aşağıdaki ifadelerden hangisi doğrudur?

A) \(\left(p \land q\right)\) B) \(\left(q' \land r\right)\) C) \(\left(p' \lor r\right)\) D) \(\left(\left(p \lor q\right)\right)^{\prime}\) E) \(\left(p \Leftrightarrow \left(q \lor r\right)\right)\)

13) Aşağıdaki ifade hangisine eşdeğerdir?
\(\left(\left(p' \land \left(q \lor p\right)\right)\right)^{\prime}\)

A) \(\left(\left(\left(r \land p\right) \lor \left(p \Rightarrow q\right)\right) \lor \left(\left(p' \land p'\right) \lor \left(r' \lor p\right)\right)\right)\) B) \(\left(\left(q \Rightarrow p'\right)\right)^{\prime}\) C) \(\left(\left(p' \oplus p'\right) \Leftrightarrow \left(\left(p \oplus r\right)\right)^{\prime}\right)\) D) \(\left(p \lor \left(q' \land p'\right)\right)\) E) \(\left(\left(\left(q' \Leftrightarrow r'\right) \land \left(q \land q\right)\right) \lor \left(\left(q' \land p'\right) \oplus \left(r \lor p\right)\right)\right)\)

14) Aşağıdaki ifade hangisine eşdeğerdir?
\(\left(\left(\left(p \lor p\right) \lor q'\right)\right)^{\prime}\)

A) \(\left(\left(q' \lor q\right) \land \left(r' \Rightarrow q'\right)\right)\) B) \(\left(\left(\left(r' \Leftrightarrow r\right)\right)^{\prime} \oplus \left(r \land q'\right)\right)\) C) \(\left(\left(q \lor q'\right) \oplus \left(p \lor r'\right)\right)\) D) \(\left(\left(p' \land p'\right) \land q\right)\) E) \(\left(\left(q' \oplus r'\right)\right)^{\prime}\)

15) Aşağıdaki ifade hangisine eşdeğerdir?
\(\left(\left(q \land \left(p \lor r\right)\right)\right)^{\prime}\)

A) \(\left(\left(r \land r'\right) \lor \left(p' \Rightarrow q\right)\right)\) B) \(\left(\left(p \land r\right) \lor \left(q' \lor r\right)\right)\) C) \(\left(\left(\left(q' \lor r\right) \Leftrightarrow \left(r \land q\right)\right) \land \left(\left(p \land q\right) \land \left(p' \lor q\right)\right)\right)\) D) \(\left(q' \lor \left(p' \land r'\right)\right)\) E) \(\left(\left(\left(r' \land p'\right) \land \left(q \Rightarrow r\right)\right) \lor \left(\left(q \lor p\right) \Rightarrow r'\right)\right)\)

16) p, q ve r önermeleri için p = Yanlış, q = Doğru, r = Doğru iken, aşağıdaki ifadelerden hangisi doğrudur?

A) \(\left(\left(p \lor q\right)\right)^{\prime}\) B) \(\left(p \oplus q\right)\) C) \(\left(p \land q\right)\) D) \(\left(p \Leftrightarrow \left(q \lor r\right)\right)\) E) \(\left(q' \land r\right)\)

17) Aşağıdaki ifade hangisine eşdeğerdir?
\(\left(\left(q' \lor q'\right)\right)^{\prime}\)

A) \(\left(\left(p \lor p\right) \lor p\right)\) B) \(\left(q \land q\right)\) C) \(\left(\left(\left(r' \Leftrightarrow r\right) \Leftrightarrow \left(q \Rightarrow r\right)\right)\right)^{\prime}\) D) \(\left(\left(p' \Rightarrow r'\right) \lor \left(\left(q' \lor r\right) \land \left(p \land p'\right)\right)\right)\) E) \(\left(\left(r' \lor p'\right)\right)^{\prime}\)

18) Aşağıdaki ifade hangisine eşdeğerdir?
\(\left(\left(\left(p' \land r\right) \land q\right)\right)^{\prime}\)

A) \(\left(\left(p \lor r'\right) \lor q'\right)\) B) \(\left(\left(\left(p' \lor r'\right) \land \left(p \land q\right)\right) \Leftrightarrow \left(\left(p' \Leftrightarrow r\right) \land \left(p' \land p\right)\right)\right)\) C) \(\left(\left(\left(q \Leftrightarrow r\right) \Rightarrow \left(r \Rightarrow p\right)\right) \Rightarrow \left(\left(p' \Leftrightarrow q'\right) \land \left(q \land q'\right)\right)\right)\) D) \(\left(\left(\left(q' \land p'\right) \lor \left(p' \lor r'\right)\right) \oplus \left(\left(p' \Rightarrow p'\right) \land q'\right)\right)\) E) \(\left(\left(\left(q \land q\right) \land \left(r \oplus r'\right)\right) \Leftrightarrow \left(q \oplus \left(q' \Leftrightarrow r\right)\right)\right)\)

19) p, q ve r önermeleri için p = Yanlış, q = Doğru, r = Yanlış iken, aşağıdaki ifadelerden hangisi doğrudur?

A) \(\left(q' \land r\right)\) B) \(\left(p \Leftrightarrow q\right)\) C) \(\left(p \land q\right)\) D) \(\left(\left(p \land q\right) \Rightarrow r\right)\) E) \(\left(p \land \left(q \lor r\right)\right)\)

20) p, q ve r önermeleri için p = Doğru, q = Yanlış, r = Yanlış iken, aşağıdaki ifadelerden hangisi doğrudur?

A) \(\left(p \land \left(q \lor r\right)\right)\) B) \(\left(\left(p \land q\right) \Rightarrow r\right)\) C) \(\left(p \Leftrightarrow \left(q \lor r\right)\right)\) D) \(\left(p \land q\right)\) E) \(\left(p \Leftrightarrow q\right)\)