Argument Lecture 5 Example An interesting teacher keeps
- Slides: 23
Argument Lecture 5
Example • An interesting teacher keeps me awake. I stay awake in XYZ class. Therefore, my XYZ teacher is interesting. • Is the above argument valid?
Definition • An argument is a sequence of declarative sentences • One of which is intended as a conclusion • The remaining sentences, the premises, are intended to prove or at least provide some evidence for the conclusion.
ARGUMENT: • An argument is a list of statements called premises (or assumptions or hypotheses) followed by a statement called the conclusion. P 1 Premise P 2 Premise P 3 Premise. . Pn Premise _______ ∴C Conclusion
VALID AND INVALID ARGUMENT: • An argument is valid if the conclusion is true when all the premises are true. • Alternatively, an argument is valid if conjunction of its premises imply conclusion. • That is (P 1∧ P 2 ∧ P 3 ∧. . . ∧ Pn) → C is a tautology. • An argument is invalid if the conclusion is false when all the premises are true. • Alternatively, an argument is invalid if conjunction of its premises does not imply conclusion.
EXAMPLE: • Show that the following argument form is valid: p→q p ∴ q
EXAMPLE • Show that the following argument form is invalid: p→q q ∴ p
EXERCISE: Use truth table to determine the argument form p∨q p → ~q p→r ∴ r is valid or invalid.
WORD PROBLEM • If Tariq is not on team A, then Hameed is on team B. If Hameed is not on team B, then Tariq is on team A. • ∴ Tariq is not on team A or Hameed is not on team B. SOLUTION Let t = Tariq is on team A , h = Hameed is on team B Then the argument is ~ t → h ~ h → t ∴ ~ t ∨ ~ h
EXERCISE • If at least one of these two numbers is divisible by 6, then the product of these two numbers is divisible by 6. Neither of these two numbers is divisible by 6. • ∴ The product of these two numbers is not divisible by 6.
EXERCISE • If I got an Eid bonus, I’ll buy a stereo. If I sell my motorcycle, I’ll buy a stereo. • ∴ If I get an Eid bonus or I sell my motorcycle, then I’ll buy a stereo
Applications of logic SWITCHES IN SERIES
SWITCHES IN PARALLEL:
SWITCHES IN SERIES:
SWITCHES IN PARALLEL:
NOT-gate • A NOT-gate (or inverter) is a circuit with one input and one output signal. If the • input signal is 1, the output signal is 0. Conversely, if the input signal is 0, then the output signal is 1.
2. AND-gate • An AND-gate is a circuit with two input signals and one output signal. • If both input signals are 1, the output signal is 1. Otherwise the output signal is 0.
OR-gate • An OR-gate is a circuit with two input signals and one output signal. • If both input signals are 0, then the output signal is 0. Otherwise, the output signal is 1
COMBINATIONAL CIRCUIT: • A Combinational Circuit is a compound circuit consisting of the basic logic gates such as NOT, AND, OR.
DETERMINING OUTPUT FOR A GIVEN INPUT: • Indicate the output of the circuit below when the input signals are P = 1, Q = 0 and R = 0
FINDING A BOOLEAN EXPRESSION FOR A CIRCUIT
CONSTRUCTING THE INPUT/OUTPUT TABLE FOR A CIRCUIT
CONSTRUCTING THE INPUT/OUTPUT TABLE FOR A CIRCUIT
- Interesting more interesting the most interesting
- Ontological vs teleological
- The teacher always . . . us interesting project work. *
- 01:640:244 lecture notes - lecture 15: plat, idah, farad
- How many units for teacher 3
- Good afternoon dear students
- What keeps the sun hot
- Romeo and juliet famous quotes
- Holds data, instructions, and information for future use.
- Hotel missing dollar riddle
- Peng wang cheese tofu calories
- Shunt voltage regulator factory
- To keeps one's temper meaning
- When everybody has short hair
- Whoever keeps his life will lose it
- Aleks math intervention
- Brian keeps the signal fire burning days and nights.
- Force that keeps each tire from sliding on the road
- Type 1 error and type 2 error in statistics
- Force that keeps each tire from sliding on the road
- A new settlement that keeps close ties to its homeland
- Plus minus interesting example
- Plus minus interesting example
- Invalid statement examples