We remember that a knight is a person who always tells the truth, and a knave is a person who always lies. When we say that two people are of the same type, it means that they are both knights or both knaves. When they are said to be of different types, it means that one of them is a knight and the other is a knave. You meet two people, A and B. A said: "If B is a knave, then I am a knight." B says, "A and I are different types" What are the identities of A and B? A. A is a knight and B is a knight. B. A is a knight and B is a knave. C. A is knave and B is knight. D. A is knave and B is knave. E. It is impossible to determine the identity of A and B. F. none of the above Let A= {1,3,5}, B = {2,4,6,8), C= {2,3,4,5) Which of the following statements is false? A. AnB = 0 B. |ANC| = |BnC| C. |P(C) = 16 D. C-BCA E. BCAUC E|AX C| = 12
We remember that a knight is a person who always tells the truth, and a knave is a person who always lies. When we say that two people are of the same type, it means that they are both knights or both knaves. When they are said to be of different types, it means that one of them is a knight and the other is a knave. You meet two people, A and B. A said: "If B is a knave, then I am a knight." B says, "A and I are different types" What are the identities of A and B? A. A is a knight and B is a knight. B. A is a knight and B is a knave. C. A is knave and B is knight. D. A is knave and B is knave. E. It is impossible to determine the identity of A and B. F. none of the above Let A= {1,3,5}, B = {2,4,6,8), C= {2,3,4,5) Which of the following statements is false? A. AnB = 0 B. |ANC| = |BnC| C. |P(C) = 16 D. C-BCA E. BCAUC E|AX C| = 12
Transcribed Image Text:We remember that a knight is a person who always tells the truth, and a knave is a
person who always lies. When we say that two people are of the same type, it means
that they are both knights or both knaves. When they are said to be of different types,
it means that one of them is a knight and the other is a knave. You meet two people,
A and B.
A said: "If Bis a knave, then I am a knight."
B says, "A and I are different types"
What are the identities of A and B?
A. A is a knight and B is a knight.
B. A is a knight and B is a knave.
C. A is knave and B is knight.
D. A is knave and B is knave.
E. It is impossible to determine the identity of A and B.
F. none of the above
Let
A = {1,3,5}, B = {2,4,6,8), C=(2,3,4,5)
Which of the following statements is false?
A. AnB = 0
B. ANC| = |Bnc|
C.
|P(C) = 16
D. C-BCA
E. BCAUC
F. |AX C| = 12
Transcribed Image Text:Letz and y be propositional variables, and let
P₁: zvy
P₂:x^-y
P3: y → z
C:y
Answer the following three questions, in order:
Is the argument (P^ P₂^ Ps) → C valid?
• Is the set {P₁, P₂, P3} consistent?
• Are P₂ and -P3 logically equivalent?
A. Yes, no, yes.
B. No, yes, yes.
C. No, yes, no.
D. Yes, no, no.
E. Yes, yes, yes.
F. No, no, yes.
G. none of the above.
Recall that a binary string is a sequence of 0's and 1's. How many binary strings of
length 8 have starting with "0000"?
A. 8!
B. 28
C.
D. 5!
E. 2¹
E8-7-6-5-4
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