Discrete Mathematics

Master-theorem is not allowed, I need it showed by induction weather one of the 1,2,3 is right. Pls step by step.

The title explains it. Prove that : $ \sum_{k=1}^{\infty} {(-1)^k\rm e}^{-\hat{t} k^2} \geq \frac{2}{\pi}\ \sum_{k=1}^{\infty} \frac{(-1)^k}{2k-1}{\rm e}^{\frac{-\hat{t} (2k-1)^2}{4}}  $ for $\hat{t}&...

Please answer with all the conditions.

Let A be an uncountable set, B a countable subset of A, and C the complement of B in A. Prove that there exists a one-to-one correspondence between A and C.

Can you explain how to answer these questions i have the final answer but i don't know how they reach to it

Problem 1. Suppose we draw 9 cards from a standard 52-card deck. Find the probability that your 9-card hand consists of exactly 4 (distinct) pairs. Assume the cards are drawn at the same time (so orde...

1)Find the number of factor trees of the graph below2)Given the graph G of the figure below. What is the number of factor trees of G that contain the path 2-3-4-5-6-7-11 ?3)Suppose we want to schedule...

1) Let $T$ be a tree with 47 vertices with the property that removing a vertex (and its adjacent edges) from $T $ creates two coherent components $T_1,T_2$ which are also trees. For$ i=1,2,$ we denote...

Need help for introductory level discrete math course, proof by induction only. See attachment for details

Please help me with the question attached below.

I need help with the question below. I would really appreciate if you can solve it for me. 

Need Help with the discrete math question in the image below. You need to use the Deza-Frankl-Singhi theorem to solve it. 

1) Let G be the graph whose vertices are all permutations of the integers of the set {1,2,…,10} with the property that two vertices (ε1,ε2,…,ε10) , (ε′1,ε′2, ...,ε′10) are connected by an edge if one...

Need Help with the question attached in image. 

I can't seem to figure out how to answer this question. I would really appreciate it if you can solve it for me. Here is the question: Let A ⊂ [9]^(3) with |A| = 28. How small can the lower shadow of...

(𝐴→𝐶)∧(𝐵→𝐶)⊢(𝐴∧𝐵)→𝐶The proof should be in this format https://www.google.com/search?q=box+proof&sxsrf=ALiCzsbWeLPgtJKBnefv_2tWdCrdIvNukg:1667929483758&source=lnms&tbm=isch&sa=X&ved...

A v ¬A the proof should be in this formathttps://www.google.com/search?q=box+proof&sxsrf=ALiCzsbWeLPgtJKBnefv_2tWdCrdIvNukg:1667929483758&source=lnms&tbm=isch&sa=X&ved=2ahUKEwjq3o7...

𝐴→(𝐵→𝐶),𝐴→𝐵,𝐴⊢𝐶the proof should be in this format https://www.google.com/search?q=box+proof&sxsrf=ALiCzsbWeLPgtJKBnefv_2tWdCrdIvNukg:1667929483758&source=lnms&tbm=isch&sa=X&ved=2ah...

𝐴∧(𝐵∨𝐶)⊢(𝐴∧𝐵)∨(𝐴∧𝐶)answer should be in this format https://www.google.com/search?q=box+proof&sxsrf=ALiCzsbWeLPgtJKBnefv_2tWdCrdIvNukg:1667929483758&source=lnms&tbm=isch&sa=X&ved=2a...

𝐴∨𝐵→𝐶⊢(𝐴→𝐶)∧(𝐵→𝐶)the proof should be in this formathttps://www.google.com/search?q=box+proof&sxsrf=ALiCzsbWeLPgtJKBnefv_2tWdCrdIvNukg:1667929483758&source=lnms&tbm=isch&sa=X&ved=2a...

¬¬𝐴→𝐴 the proof should be in this format https://www.google.com/search?q=box+proof&sxsrf=ALiCzsbWeLPgtJKBnefv_2tWdCrdIvNukg:1667929483758&source=lnms&tbm=isch&sa=X&ved=2ahUKEwjq3o7...

The answer should have a completely annotated box proof(𝐴→(𝐵→𝐶))→((𝐴→𝐵)→(𝐴→𝐶))

1) In how many ways can we place 19 numbered balls in 5 boxes, 3 of which have a capacity of 3 and the other 2 have a capacity of 5 if the boxes are not numbered? 2)How many subsets A of {1,2,…,28} ar...

1st-year undergraduate combinatorics. 

Hi I must take a quiz in the next 20 hours and wanted to check if anyone here feels confident in that subject (I don't know the length of the quiz but I'm going to compensate accordingly), 1 or 2 ques...