math55-spring_2004-mt1-Demmel-soln

math55-spring_2004-mt1-Demmel-soln - Math 55 First Midterm...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 55 First Midterm 17 Feb 2004 NAME (1 pt): TA (1 pt): Name of Neighbor to your left (1 pt): Name of Neighbor to your right (1 pt): Instructions : This is a closed book, closed notes, closed calculator, closed computer, closed network, open brain exam. You get one point each for filling in the 4 lines at the top of this page. All other questions are worth 12 points. Write all your answers on this exam. If you need scratch paper, ask for it, write your name on each sheet, and attach it when you turn it in (we have a stapler). 1 2 3 4 5 Total 1 Question 1) (12 pts) Determine whether or not the following proposition is a tautology. a b means the exclusive or of a and b . ( q ( p r )) ( p r ) If it is, prove it using rules for simplifying logical expressions, not using a truth table. If not, give a counterexample. Indicate what you are doing at each step (i.e. you dont need to know the Latin names of inference rules, just convince us that you know what youre doing). You may use the rule that ( a b ) is logically equivalent to either ( a ) b or a ( b ). Answer: ( q ( p r )) ( p r ) (definition of ) ( q ( p r )) ( p r ) (DeMorgans Law) ( q ( p r )) ( p r ) (rule that ( p r ) same as ( p ) r ) ( q ( p r )) ( p r ) (definition of ) ( q (( p r ) ( p r )) ( p r ) (double negative) ( q (( p r ) ( p r )) ( p r ) (DeMorgans Law) ( q ( ( p r ) ( p r )) ( p r ) (associativity and commutativity of ) (( p r ) ( ( p r )) ( p r ) q ( x x is always true, where x = p r ) ( T ) ( p r ) q ( T x is always true, for any x ) T 2 Question 1) (12 pts) Determine whether or not the following proposition is a tautology. c d means the exclusive or of c and d . (( t r ) s ) ( t r ) If it is, prove it using rules for simplifying logical expressions, not using a truth table. If not, give a counterexample. Indicate what you are doing at each step (i.e. you dont need to know the Latin names of inference rules, just convince us that you know what youre doing). You may use the rule that ( c d ) is logically equivalent to either ( c ) d or c ( d ). Answer: ( s ( t r )) ( t r ) (definition of ) ( s ( t r )) ( t r ) (DeMorgans Law) ( s ( t r )) ( t r ) (double negative) ( s ( t r )) ( t r ) (rule that ( t r ) same as ( t ) r ) ( s ( t r )) ( t r ) (definition of ) ( s (( t r ) ( t r )) ( t r ) (double negative) ( s (( t r ) ( t r )) ( t r ) (DeMorgans Law) ( s (...
View Full Document

This note was uploaded on 03/08/2010 for the course MATH 55 taught by Professor Strain during the Spring '08 term at University of California, Berkeley.

Page1 / 16

math55-spring_2004-mt1-Demmel-soln - Math 55 First Midterm...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online