pset1_soln

pset1_soln - 6.042/18.062J Mathematics for Computer Science...

Info iconThis preview shows pages 1–3. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 6.042/18.062J Mathematics for Computer Science February 1, 2005 Srini Devadas and Eric Lehman Problem Set 1 Solutions Due: Monday, February 7 at 9 PM Problem 1. The connectives (and), (or), and (implies) come often not only in com- puter programs, but also everyday speech. But devices that compute the nand operation are preferable in computer chip designs. Here is the truth table for nand: P Q T T F T F T F T T F F T P nand Q For each of the following expressions, find an equivalent expression using only nand and (not). (a) A B Solution. ( A nand B ) (b) A B Solution. ( A ) nand ( B ) (c) A B Solution. A nand ( B ) Problem 2. A self-proclaimed great logician has invented a new quantifier, on par with (there exists) and (for all). The new quantifier is symbolized by U and read there exists a unique. The proposition Ux P ( x ) is true iff there is exactly one x for which P ( x ) is true. The logician has noted, There used to be two quantifiers, but now there are three! I have extended the whole field of mathematics by 50%! (a) Write a proposition equivalent to Ux P ( x ) using only the quantifier, =, and logical connectives. Solution. x ( P ( x ) ( y ( ( x = y ) P ( y ))) 2 Problem Set 1 (b) Write a proposition equivalent to Ux P ( x ) using only the quantifier, =, and logical connectives. Solution. = y P ( y ))) x ( P ( x ) y ( x Problem 3. A media tycoon has an idea for an all-news television network called LNN: The Logic News Network. Each segment will begin with the definition of some relevant sets and predicates. The days happenings...
View Full Document

Page1 / 5

pset1_soln - 6.042/18.062J Mathematics for Computer Science...

This preview shows document pages 1 - 3. Sign up to view the full document.

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