ITEC 122 2007fall ibarland

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Although you are welcome to typeset your work nicely (using Microsoft Word or LaTeX or whatever to get nice logic symbols), it's probably much easier to write formulas by hand.

(Trouble reading some symbols on this page? Here's a screen shot.)

1. TeachLogic exercises I: #21 (algebra).
   You may justify each step by either using the rules named as , or as in Rosen's §1.2 tables 6,7,8.
   (Your answers will be in the same format as the problems in Rosen section 1.2, examples 5,6,7,8 and TeachLogic: propositional algebra.
2. TeachLogic exercises I: #9 (ebay queries).
3. Rosen p.46, #5 (5ed: p.40,#5):
   Let P(x) be the statement “x spends more than 5 hours every weekday in class”, where the domain consists of Radford students. Express each of these quantifications in English.
   1. ∃x . P(x)
   2. ∀x . P(x)
   3. ∃x . ¬ P(x)
   4. ∀x . ¬ P(x)
4. Rosen p.40 #12:
   Let Q(x) be the statement “x+1 > 2x”. If the domain is the set of integers Z = {…,-2,-1,0,+1,+2,…}, what are these truth values?
   1. true or false?: Q(0)
   2. true or false?: Q(-1)
   3. true or false?: Q(1)
   4. true or false?: ∃x . Q(x)
   5. true or false?: ∀x . Q(x)
   6. true or false?: ∃x . ¬Q(x)
   7. true or false?: ∀x . ¬Q(x)
5. Rosen p. 51, #1
   Translate these statements into English:
   1. ∀x . ∃y . (x < y)
   2. ∀x . ∀y . (((x≥0) ∧ (y≥0) ) → (x·y ≥ 0))
   3. ∀x . ∀y . ∃ z . (x·y = z)
   4. Not in book: ∀x . ∀y . ∃ z . (x/y = z)
6. For each of the four statements above, is it true when the domain¹ is all real numbers ℜ? How about when the universe of discourse is restricted to the natural numbers N = {0,1,2,3,…}? ²
7. Rosen #26.
   Let Q(x, y) be the statement “x+y = x-y”. If the domain is the set of integers Z = {…,-2,-1,0,+1,+2,…}, what are the truth values?
   1. Q(1, 1)
   2. Q(2, 0)
   3. ∀y . Q(1, y)
   4. ∀x . Q(x, 2)
   5. ∃x . ∃y . Q(x,y)
   6. ∀x . ∃y . Q(x,y)
   7. ∃y. ∀x . Q(x, y)
   8. ∀y . ∃x . Q(x,y)
   9. ∀x . ∀y . Q(x,y)

If you see a few other problems in Rosen which catch your eye, and you'd like to do them for extra credit, you are welcome to (though you can ask me for how much; extra-credit is harder to earn point-per-point than regular credit).

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©2007, Ian Barland, Radford University Last modified 2007.Dec.17 (Mon)

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