The Foundations: Logic and Proofs
... Showing that f is one-to-one or onto Example 1: Let f be the function from {a,b,c,d} to {1,2,3} defined by f(a) = 3, f(b) = 2, f(c) = 1, and f(d) = 3. Is f an onto function? Solution: Yes, f is onto since all three elements of the codomain are images of elements in the domain. If the codomain were ...
... Showing that f is one-to-one or onto Example 1: Let f be the function from {a,b,c,d} to {1,2,3} defined by f(a) = 3, f(b) = 2, f(c) = 1, and f(d) = 3. Is f an onto function? Solution: Yes, f is onto since all three elements of the codomain are images of elements in the domain. If the codomain were ...
Section 9.2: Summation Notation
... It is an arithmetic sequence with first term a = 1 and common difference d = 1. ...
... It is an arithmetic sequence with first term a = 1 and common difference d = 1. ...
Haskell
... The output of your function should be a list consisting of the names of the students whohave issued at least one bookduring the current semester. This list need not be in any specific order but it should not have any duplicate entries. You may assume that no 2 students have the same name. (6 marks) ...
... The output of your function should be a list consisting of the names of the students whohave issued at least one bookduring the current semester. This list need not be in any specific order but it should not have any duplicate entries. You may assume that no 2 students have the same name. (6 marks) ...
MATH 363 Discrete Mathematics SOLUTIONS : Assignment 3 1
... and so p3 = 2q 3 is even. We conclude that p is also even, (if p was odd, then p3 would also be odd). Say p = 2m, then 8m3 = 2q 3 and thus, q 3 is even. Similarly, we have that q is even. But this √ is a contradiction to the assumption that p and q have no common factors. Therefore we conclude that ...
... and so p3 = 2q 3 is even. We conclude that p is also even, (if p was odd, then p3 would also be odd). Say p = 2m, then 8m3 = 2q 3 and thus, q 3 is even. Similarly, we have that q is even. But this √ is a contradiction to the assumption that p and q have no common factors. Therefore we conclude that ...
Big Numbers
... Using the standard arithmetic operations (addition, subtraction, multiplication, division and exponentiation), what is the largest number you can make using three copies of the digit “9”? It’s pretty clear we should just stick to exponents, and given that, here are some possibilities: 999, 999 , ...
... Using the standard arithmetic operations (addition, subtraction, multiplication, division and exponentiation), what is the largest number you can make using three copies of the digit “9”? It’s pretty clear we should just stick to exponents, and given that, here are some possibilities: 999, 999 , ...
Vats Grade 8 Algebraic Expressions Clarification
... Sets of multiples are examples of arithmetic sequences. Also a set of numbers such as 1, 5, 9, 13, 17, 21, … is an example of an arithmetic sequence; the common difference between the terms is four. An arithmetic sequence can be represented by a RULE, sometimes called a FUNCTION RULE, such as y = mx ...
... Sets of multiples are examples of arithmetic sequences. Also a set of numbers such as 1, 5, 9, 13, 17, 21, … is an example of an arithmetic sequence; the common difference between the terms is four. An arithmetic sequence can be represented by a RULE, sometimes called a FUNCTION RULE, such as y = mx ...
