Question

Prove that from any set A which contains 138 distinct integers, there exists a subset B...

Prove that from any set A which contains 138 distinct integers, there exists a subset B which contains at least 3 distinct integers and the sum of the elements in B is divisible by 46. Show all your steps

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1


We apply pigeonhole principal to solve this question. See the attached image for the detailed solution.



0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Show that: (i) any set of 46 distinct 2-digit numbers contains two distinct numbers which are...
Show that: (i) any set of 46 distinct 2-digit numbers contains two distinct numbers which are relatively prime. (ii) 46 is optimal, in the sense that there exists a set of 45 distinct 2-digit numbers so that no two distinct numbers are relatively prime.
1.) Given any set of 53 integers, show that there are two of them having the...
1.) Given any set of 53 integers, show that there are two of them having the property that either their sum or their difference is evenly divisible by 103. 2.) Let 2^N denote the set of all infinite sequences consisting entirely of 0’s and 1’s. Prove this set is uncountable.
Let X be a subset of the integers from 1 to 1997 such that |X|≥34. Show...
Let X be a subset of the integers from 1 to 1997 such that |X|≥34. Show that there exists distinct a,b,c∈X and distinct x,y,z∈X such that a+b+c=x+y+z and {a,b,c}≠{x,y,z}.
Let p and q be any two distinct prime numbers and define the relation a R...
Let p and q be any two distinct prime numbers and define the relation a R b on integers a,b by: a R b iff b-a is divisible by both p and q. I need to prove that: a) R is an equivalence relation. (which I have) b) The equivalence classes of R correspond to the elements of  ℤpq. That is: [a] = [b] as equivalence classes of R if and only if [a] = [b] as elements of ℤpq I...
11. (6 Pts.) Show that if we split any 11 numbers in 5 sets, then there...
11. (6 Pts.) Show that if we split any 11 numbers in 5 sets, then there exists one set that contains a subset such that the sum of its elements is a multiple of 3.
Consider the following relation ∼ on the set of integers a ∼ b ⇐⇒ b 2...
Consider the following relation ∼ on the set of integers a ∼ b ⇐⇒ b 2 − a 2 is divisible by 3 Prove that this is an equivalence relation. List all equivalence classes.
3. (8 marks) Let T be the set of integers that are not divisible by 3....
3. Let T be the set of integers that are not divisible by 3. Prove that T is a countable set by finding a bijection between the set T and the set of integers Z, which we know is countable from class. (You need to prove that your function is a bijection.)
Let p and q be any two distinct prime numbers and define the relation a R...
Let p and q be any two distinct prime numbers and define the relation a R b on integers a,b by: a R b iff b-a is divisible by both p and q. For this relation R: Show that the equivalence classes of R correspond to the elements of  ℤpq. That is: [a] = [b] as equivalence classes of R if and only if [a] = [b] as elements of ℤpq. you may use the following lemma: If p is prime...
Real Analysis I Prove the following exercises (show all your work)- Exercise 1.1.1: Prove part (iii)...
Real Analysis I Prove the following exercises (show all your work)- Exercise 1.1.1: Prove part (iii) of Proposition 1.1.8. That is, let F be an ordered field and x, y,z ∈ F. Prove If x < 0 and y < z, then xy > xz. Let F be an ordered field and x, y,z,w ∈ F. Then: If x < 0 and y < z, then xy > xz. Exercise 1.1.5: Let S be an ordered set. Let A ⊂...
1. Let A and B be sets. The set B is of at least the same...
1. Let A and B be sets. The set B is of at least the same size as the set A if and only if (mark all correct answers) there is a bijection from A to B there is a one-to-one function from A to B there is a one-to-one function from B to A there is an onto function from B to A A is a proper subset of B 2. Which of these sets are countable? (mark all...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT