hw3solutions

# hw3solutions - EE 369 Homework #8 Solutions (Sixth Edition)...

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EE 369 Homework 3 Solutions (Sixth Edition) Section 1.4 Decide what conclusion can be reached, and justify your answer 1) All flowers are plants. Pansies are flowers. The conclusion is that pansies are plants. Proof steps: F(x) represent the relation that x is a flower P(x) represent the relation that x is a plant Pansies is a constant symbol 1. (\forall x) F(x) --> P(x) hyp 2. F(pansies) hyp 3. F(Pansies)-->P(Pansies) 1,ui 4. P(Pansies) 2,3,mp 4) Some flowers are red. Some flowers are purple. Pansies are flowers. No conclusion is possible. Just because pansies are flowers,it does not make them either red or purple. 6) Justify each step in the proof sequence for (\exists x)[P(x)-->Q(x)]-->[(\forall x)P(x)-->(\exists x)Q(x)] 1. (\exists x)[P(x)-->Q(x)] hyp 2. P(a)-->Q(a) 1,ei 3. (\forall x)P(x) deduction method hypothesis 4. P(a) 3,ui 5. Q(a) 2,4,mp 6. (\exists x)Q(x) 5,eg 9) Consider the wff (\forall y)(\exists x)Q(x,y)-->(\exists x)(\forall y)Q(x,y) a. Find an interpretation to prove that this wff is not valid. domain is the integers, Q(x,y) is "x<y"; for every y there is an x with x<y but there is no single integer x that is less than every single integer y. b. Find the flaw in the following proof of this wff. 1. (\forall y)(\exists x) Q(x,y)

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## This note was uploaded on 09/24/2009 for the course ECE 369 taught by Professor Bagchi during the Spring '08 term at Purdue University-West Lafayette.

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hw3solutions - EE 369 Homework #8 Solutions (Sixth Edition)...

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