Homework 2 Solution - MATH 74 HOMEWORK 2 SOLUTIONS 1(a)....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 74 HOMEWORK 2 SOLUTIONS 1(a). Five ways. (( a + b ) + c ) + d ( a + b ) + ( c + d ) ( a + ( b + c )) + d a + (( b + c ) + d ) a + ( b + ( c + d )) 1(b). Fourteen ways. a + ( b + ( c + ( d + e ))) a + ( b + (( c + d ) + e )) a + (( b + ( c + d )) + e ) ( a + ( b + ( c + d ))) + e a + (( b + c ) + ( d + e )) a + ((( b + c ) + d ) + e ) ( a + (( b + c ) + d )) + e ( a + ( b + c )) + ( d + e ) (( a + ( b + c )) + d ) + e ( a + b ) + ( c + ( d + e )) ( a + b ) + (( c + d ) + e ) (( a + b ) + ( c + d )) + e (( a + b ) + c ) + ( d + e ) ((( a + b ) + c ) + d ) + e There are various ways of making this listing process more systematic; feel free to ask me about it in office hours. The number of ways of grouping seven numbers is 42. (For more on the sequence 2, 5, 14, 42, . . . , Google “Catalan numbers.”) 2. For any x, y, z we have ( x * y ) * z = ( x · y + x + y ) * z by definition = ( x · y + x + y ) · z + ( x · y + x + y ) + z by definition = x · y · z + x · z + y · z + x · y
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/10/2010 for the course MATH 74 taught by Professor Courtney during the Fall '07 term at University of California, Berkeley.

Page1 / 2

Homework 2 Solution - MATH 74 HOMEWORK 2 SOLUTIONS 1(a)....

This preview shows document pages 1 - 2. Sign up to view the full document.

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