# quebec - ∼ on Z as follows a ∼ b if and only if 3 a b...

This preview shows pages 1–6. Sign up to view the full content.

Math 210 Section 011: Test #1 NAME: This test has 6 pages . The points per page are 4, 4, 5, 5, 5, 5. [4 points] Question 1. Let P be the statement “ - 4 2 = 16.” Let Q be the statement “7 < 50.” Let R be the statement “ x = 7 is the only solution of ( x - 2) 2 = 25.” Give the truth values of each of the following. P R P Q Q R ( ¬ R ) ± P ( ¬ Q ) ² 1

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

View Full Document
[2 points] Question 2a. Explicitly write out the power set of n a, { b } o . [2 points] Question 2b. Let A = { 1 , 2 , 4 , 5 , 6 , 9 } , let B = { 1 , 2 , 3 , 5 } , and let C = { 5 , 6 , 7 , 8 } . Explicitly write out the set ( A C ) × ( A B ). 2
[3 points] Question 3a. Construct a truth table for ( P Q ) ± P ( ¬ Q ) ² . [2 points] Question 3b. If X Y is false, ﬁnd the truth value of ± ( ¬ X ) Y ² ± ( ¬ X ) ( ¬ Y ) ² . 3

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

View Full Document
[1 point] Question 4a. Show that the statement A ( B C ) = ( A B ) C is false by giving an explicit counterexample. [4 points] Question 4b. Classify each of the following as true or false. If true, give a general proof. If false, explicitly give a speciﬁc counterexample. (i) True or false: If A B = A C , then B = C . (ii) True or false: If A B = A C , then B = C . 4
[5 points] Question 5. Deﬁne a relation

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.

Unformatted text preview: ∼ on Z as follows: a ∼ b if and only if 3 a + b is a multiple of 4. Prove that ∼ is an equivalence relation. 5 [5 points] Question 6. Suppose our universe of discourse is the set of all cats. Let S ( x ) be the predicate “ x loves salmon” Let T ( x ) be the predicate “ x is teachable” Let M ( x ) be the predicate “ x is missing a tail” Let W ( x ) be the predicate “ x has whiskers” Let G ( x ) be the predicate “ x has green eyes” Let K ( x ) be the predicate “Koko the gorilla likes to play with x ” Let F ( x,y ) be the predicate “ x is willing to ﬁght with y .” Express each of the following as English sentences. ∃ x ( ¬ W ( x ) ) ∀ x ( M ( x ) → K ( x ) ) ∀ x ( G ( x ) → ∃ y F ( y,x ) ) ∀ x ± W ( x ) → ( S ( x ) → T ( x ) ) ² ∀ x ± S ( x ) → ∃ y ( ¬ F ( x,y ) ∧ ¬ F ( y,x ) ) ² 6...
View Full Document

## This note was uploaded on 12/07/2011 for the course MATH 210 taught by Professor Staff during the Spring '08 term at University of Delaware.

### Page1 / 6

quebec - ∼ on Z as follows a ∼ b if and only if 3 a b...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online