(a) Write in words how to read the following out loud: {n ∈ ℤ | n is a factor of 24}

(b) Use the set-roster notation to indicate the elements in the set {n ∈ ℤ | n is a factor of 24}

(a)  

Let A = {1,2,3,4} and B = {a,b,c}. Define a function G: A → B as follows: G = {(1,b), (2,c), (3,b), (4,c)}. (a) Find G(2). (b) Draw an arrow diagram for G.

(a)  

Let A = {3,5,7} and B = {15,16,17,18}, and define a relation R from A to B as follows: For all (x,y) ∈ A × B, (x,y) ∈ R ↔ y/x is an integer.

(a) Is 3 R 15? Is 3 R 16? Is (7,17) ∈ R? Is (3,18) ∈ R? explain.

(a)  

Given this circuit: Find output of circuit if inputs: P = 1, Q = 0 and R = 1

(a)  

Write boolean expression for the given circuit below:

(a)  

Write equivalent in decimal of the binary number 101011?

(a)  

Write result for 101112 + 10112 = (a)   .

Use the 8-bits two's complement to find 62 + (-18) = (a)   .

Let R(m,n) be the predicate "If m is a factor of $$n^2$$ then m is a factor of n with domain for both m and n be Z - the set of integers. a) Explain why R(m,n) is false when m = 25 and n = 10.

Let R(m,n) be the predicate "If m is a factor of n2n2 then m is a factor of n with domain for both m and n be Z - the set of integers. b)Give a value for m and n where R(m,n) is true. Show working.

Find counter-example to show this statement is false. ∀ positive integers m and n, m^n + n^m = 2 m + n

Rewrite in the TWO forms "∀x, if _____ then _____" and "∀x, _____ ⇒ _____" a) Every CS55 student needs to take CSP17

Write negation of "∀ real number x, if x > 3 then $$x^2$$ > 9

(a)  

Write (a) contrapositive (b) converse and (c) inverse. And also state whether each is true or false. If false, give one counter-example. ∀ integer d, if 6/d is an integer then d = 3

Assume p = x > -2 and q= x < 7. What is P ^ Q and it's negation written in words?

Given, If P is a square, then P is a rectangle

A) Write negation

(a)  

Given, If P is a square, then P is a rectangle

B) Write contrapositive

(a)  

Given, If P is a square, then P is a rectangle

C) Write inverse

(a)  

Given, If P is a square, then P is a rectangle

D) Write converse

(a)  

Prove that the addition of two odd integers is even.

Prove that 0.123123123123... is rational

Prove that the product of two rational numbers is rational

Prove that if b is divisible by a (a | b)and

c is divisible by b (b | c)

then c is divisible by a (a | c)

Let A = {3,5,7} and B = {15,16,17,18}, and define a relation R from A to B as follows: For all (x,y) ∈ A × B, (x,y) ∈ R ↔ y/x is an integer. (b) Write R as a set of ordered pairs.

(a)  

Let A = {3,5,7} and B = {15,16,17,18}, and define a relation R from A to B as follows: For all (x,y) ∈ A × B, (x,y) ∈ R ↔ y/x is an integer. (c) Write the domain and co-domain of R. (answer: "{}, {}")

(a)  

Let A = {3,5,7} and B = {15,16,17,18}, and define a relation R from A to B as follows: For all (x,y) ∈ A × B, (x,y) ∈ R ↔ y/x is an integer. (e) Is R a function from A to B? Explain.

HW 4.6

(a)  

prove $$\sqrt{\ 2}$$ is irrational

use euclidean algorithm to calculate gcd(1177,509)

(a)