Quiz2

pdf

School

City College of San Francisco *

*We aren’t endorsed by this school

Course

115

Subject

Electrical Engineering

Date

Feb 20, 2024

Type

pdf

Pages

4

Uploaded by ConstableJellyfishMaster2657

Report
Question T T7IPC “It's 3PM" is a proposition. True False Question 2 1/1pts Ahalf-adder circuit has input values of a and b, and the circuit has output values of ¢ and d. The output d is defined to be a XOR b Answer 1: XOR Question 3 1/1pts Suppose that an evironment, v, assigns V(P) = True, v(Q) = True, and v(R) = False for propositions P, Q, and R. What s the truth value of the following expression? (NOT(P AND Q) OR (R XOR NOT(Q)) True False Question 4 1/1pts Two propositional formulas are equivalent if and only if they have the same truth value in all environments. True False
When describing a propositional formula, the terms satisfiable and valid have the same meaning. True False Question 6 1/1pts Given any propositional formula, there is always a fast (in polynomial time) way of checking whether or not the formula is satisfiable. True False Question 7 1/1pts The following statements are logically equivalent: e If1am hungry, then | am grumpy. * If I am not grumpy, then | am not hungry. True False Question 8 1/1pts Every propositional formula is equivalent to both a ful disjunctive normal form and a full conjunctive normal form. True False Question 9 1/1pts For the predicate P(x, y) that P(x, y) is true. [x + 2 = y], choose all the pairs of x and y such
Question 14 1/1pts The statement: NOT(¥x. P(x)) is equivalent to 3x. NOT(P(x)) is a representation of which of the following. De Morgan's Laws for Quantifiers modus ponens Goldbach's Conjecture Question 15 1/1pts The statement: Vydx. P(x,y) = 3xVy. P(x,y) is not valid. Choose the most reasonable method for proving this statement is not valid for any domain in general. Check the truth value for every pair of domain values x, y Find a pair of domain values x, y such that y3x. P(x, y) is true and 3xVy. P(x, y) is false. Find a pair of domain values x, y such that 3xVy. P(x, y) is true and Vy3x. P(x,y) is false.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Question 10 1/1pts Let x, y range over N and define Q(y) ::= Jx. x < y. Choose all the values for y such that Q(y) is true. Question 11 1/1pts For G ::= Vx3y. x < y, choose all the domains that ensure G is true. The natural numbers The negative integers The real numbers Question 12 1/1pts If you can prove that the predicate P(c) is true for some arbitrary domain value c, then you can conclude that Vx. P(x). True False Question 13 1/1pts The counter-model: e domain ::= {1, 2} e Q(z)=z=1],P(z) ==z =2] proves that Vz. [P(z) V Q(z)] = [Vx. P(x) VvV Vy. Q(y)] is not valid. True False