Question

In: Advanced Math

Let S{a, b, c, d} be a set of four positive integers. If pairs of distinct...

Let S{a, b, c, d} be a set of four positive integers. If pairs of distinct elements of S are added, the following six sums are obtained:5,10, 11,13,14,19. Determine the values of a, b, c, and d. (There are two possibilities. )

Solutions

Expert Solution


Related Solutions

8.Let a and b be integers and d a positive integer. (a) Prove that if d...
8.Let a and b be integers and d a positive integer. (a) Prove that if d divides a and d divides b, then d divides both a + b and a − b. (b) Is the converse of the above true? If so, prove it. If not, give a specific example of a, b, d showing that the converse is false. 9. Let a, b, c, m, n be integers. Prove that if a divides each of b and c,...
Let a and b be positive integers, and let d be their greatest common divisor. Prove...
Let a and b be positive integers, and let d be their greatest common divisor. Prove that there are infinitely many integers x and y such that ax+by = d. Next, given one particular solution x0 and y0 of this equation, show how to find all the solutions.
Let A[1..n] be an array of distinct positive integers, and let t be a positive integer....
Let A[1..n] be an array of distinct positive integers, and let t be a positive integer. (a) Assuming that A is sorted, show that in O(n) time it can be decided if A contains two distinct elements x and y such that x + y = t. (b) Use part (a) to show that the following problem, re- ferred to as the 3-Sum problem, can be solved in O(n2) time: 3-Sum Given an array A[1..n] of distinct positive integers, and...
Prove or disprove: If a, b, c are any three distinct positive integers such that 1/a...
Prove or disprove: If a, b, c are any three distinct positive integers such that 1/a + 1/b + 1/c = 1, then a + b + c is a prime
Prove or disprove: If a, b, c are any three distinct positive integers such that 1/a...
Prove or disprove: If a, b, c are any three distinct positive integers such that 1/a + 1/b + 1/c = 1, then a + b + c is a prime.
Let S = {a, b, c, d} and P(S) its power set. Define the minus binary...
Let S = {a, b, c, d} and P(S) its power set. Define the minus binary operation by A − B = {x ∈ S | x ∈ A but x /∈ B}. Show that (by counter-examples) this binary operation is not associative, and it does not have identity
Show that if a, b are positive integers and d = hcf(a, b), then there are...
Show that if a, b are positive integers and d = hcf(a, b), then there are positive integers s, t such that d = sa − tb.
Let us choose seven arbitrary distinct positive integers, not exceeding 24. Show that there will be...
Let us choose seven arbitrary distinct positive integers, not exceeding 24. Show that there will be at least two subsets chosen from these seven numbers with equal total sums. (Keep in mind that sets, and hence subsets, have no repeated elements.) Hint: How many subsets can you form altogether? What is the largest total sum of such a subset?
Let An = {ai} n i=1 denote a list of n distinct positive integers. The median...
Let An = {ai} n i=1 denote a list of n distinct positive integers. The median mA of An is a value in An such that half the elements in An are less than m (and so, the other half are greater than or equal m). In fact, the median element is said to have a middle rank. (a) Develop an algorithm that uses Sorting to return mA given An. (6%) (b) Now assume that one is given another list...
Let S = {a, b, c}. Draw a graph whose vertex set is P(S) and for...
Let S = {a, b, c}. Draw a graph whose vertex set is P(S) and for which the subsets A and B of S are adjacent if and only if A ⊂ B and |A| = |B| − 1. (a) How many vertices and edges does this graph have? (b) Can you name this graph? (c) Is this graph connected? (d) Does it have a perfect matching? If yes, draw a sketch of the matching. (e) Does it have a...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT