{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

09-07-homework-1

# 09-07-homework-1 - 2 ±or each of the following four...

This preview shows page 1. Sign up to view the full content.

Sets and Logic — Fall 2011 due Wednesday, 9/15/11 Homework #1 1 This problem has three parts. a. Analyze the logical form of the statement If it is raining, then it is windy and the sun is not shining. b. Analyze the logical form of the statement Rain is a sufficient condition for wind with no sunshine. Is this statement equivalent to the statement in part a? c. Analyze the logical form of the statement Rain is a necessary condition for wind with no sunshine. Is this statement equivalent to the statement in part a?
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2 ±or each of the following four propositions, determine if they are true or false for all natural numbers. a. ∀ x ∃ y (2 x-y = 0). b. ∀ x ( x < 10-→ ∀ y ( y < x-→ y < 9)). c. ∃ y ∃ z ( y + z = 100). d. ∀ x ∃ y ( y > x ∧ ∃ z ( y + z = 100)). 3 Show that the statements A ⊆ B and A \ B = ∅ are equivalent by writing each in logical symbols and then showing that the resulting formulas are logically equivalent....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online