Symbolic Arguments

• Consider an argument in the form:

          If the car is a Road Runner, then the car is fast.
  	The car is fast
  	∴ the car is a Road Runner
      

• Is this argument valid?
• To test the validity of an argument
  • Represent each statement symbolically

    p = The car is a Road Runner
    q = The car is fast
       p → q
       q
        ∴ p
    	

  • Build a truth table for stmt₁ ∧ stmt₂ ... ∧ stmt_n → conclusion

    p	q	p→ q	(p→ q) ∧ q	[(p→ q) ∧ q] → p
    T	T	T	T	T
    T	F	F	F	T
    F	T	T	T	F
    F	F	T	F	T

  • If the statement is a tautology, then the argument is correct. If not, then the argument is not correct.
• A correct argument is valid
• Do page 160 problem 37, 39, 43, 59

Switching Circuits

• Describe and

      _____/ ______/ ______0
      

• Describe or

          _______/ ______
      ____|             |____0
          |______/ _____|
  
      

• Do Page 174 problems 5-20