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Category > Math Posted 19 Apr 2017 My Price 8.00

Create truth tables for the following statements

i need help with my math homework which is due today at 3pm. thank you

 

 

 
Math 140: Homework 1 (Due Sept 14) Name: Instructions: Staple all work to the back of this page.
Problem 1: Create truth tables for the following statements.
a. (p ∨ q)∧ ∼ p
b. ∼ (p ∧ q) ∨ p
c. (p ∨ q) ∧ (q ∨ r)
Problem 2: Show that the following are logically equivalent by means of a truth table:
a. p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r (i.e. The Associative Law Holds)
b. ∼ (p ∧ q) ∧ p ≡ ∼ q ∧ p
c. ∼ (p ∨ (∼ q ∧ ∼ r)) ≡∼ p ∧ (q ∨ r)
Problem 3: Use truth tables to determine which of the following are tautologies and which are contradictions.
a. (p ∧ q) ∨ (∼ p ∨ (p ∧ ∼ q))
b. (p ∧ ∼ q) ∧ (∼ p ∨ q)
c. ((∼ p ∧ q) ∧ (q ∧ r)) ∧ ∼ q
d. (∼ p ∨ q) ∨ (p ∧ ∼ q)
Problem 4: (The Definition of Exclusive-Or) Let p⊕q be shorthand for the statement (p∨q) ∧ ∼ (p∧q).
a. By writing a truth table for (p ∨ q) ∧ ∼ (p ∧ q) verify that:
p
T
T
F
F q
T
F
T
F p⊕q
F
T
T
F You may view the truth table above as the definition of p ⊕ q; this is the notion of “exclusive-or”: p
or q is true but not both. It may be easier to think of p ⊕ q as being true when exactly one of p or q
is true. Answer the following questions about the algebraic structure of exclusive-or.
b. Is (p ⊕ q) ⊕ r ≡ p ⊕ (q ⊕ r)? (i.e. Is ⊕ associative?) Justify by a truth table if it is true, or find specific
truth values for p, q, and r which would show that they aren’t equivalent.
c. Is (p ⊕ q) ∧ r ≡ (p ∧ r) ⊕ (q ∧ r)? (i.e. Does ∧ distribute over ⊕?) Justify by a truth table if it is true,
or find specific truth values for p, q and r which would show that they aren’t equivalent.

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ComputerScienceExpert
(11)
Status NEW Posted 19 Apr 2017 05:04 AM My Price 8.00

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