{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

2_-_Solutions

# 2_-_Solutions - Assignment 2 Solutions 1 Negate the...

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

Assignment 2 – Solutions 1. Negate the expression x y, ( P ( x ) OR Q ( y )) and simplify your answer. Solution: NOT x y, ( P ( x ) OR Q ( y )) x y, NOT ( P ( x ) OR Q ( y )) x y, (NOT P ( x )) AND (NOT Q ( y )) 2. For each of the following statements, determine whether it is true when the universe of discourse is Z and whether it is true when the universe of discourse is R . (a) x y ( x = y 3 ) Solution: This is false in Z , for example when x = 2 there is no integer y for which x = y 3 . On the other hand, it is true in R . Indeed given x R we can choose y = 3 x and then we have x = y 3 . (b) x y ( y < x AND z ( z < x = z y ) ) Solution: This is true in Z . Indeed given x Z we can choose y = x - 1. Then we have y < x , and for all z Z , if z < x then we have z x - 1, that is z y . On the other hand, the given statement is false in R . Indeed given x R and given y R with y < x , we can choose z R with y < z < x (for example we can choose z = x + y 2 ).

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}