Discrete Mathematics Answers

11 integers are arbitrarily chosen. Prove that 2 of them have the same unit digit

Consider the following sequence of successive numbers of the 2k -th power: 1, 2^2k, 3^2k, 4 ^2k, 5 ^2k, ... Show that the difference between the numbers in this sequence is odd for all k ∈ N.

“The product of two odd numbers is odd.”
Using Direct proof method

The sum of two even numbers is even.
Using Direct proof method

make a truth table
(~p∧q) ∨ (p∧~q)

Statement: “If n is any even integer, then ”
Using Direct proof method

a) How many cards must be selected from a standard deck of 52 cards to guarantee that at least three cards of the same suit are chosen? b) How many must be selected to guarantee that at least three hearts are selected?

01. A) Let a, b, and c be integers, where a = 0. Then (i) If a | b and a | c, then a | (b + c); (ii) If a | b, then a | bc for all integers c; (iii) If a | b and b | c, then a | c. Course Code: CSE-1102 B) Use Algorithm of Modular Exponentiation to find 1231001 mod 101

Given: An=3an-1 - 4an-3 + f(n) find the particular soulution an^(p) when a) f(1) = n2(2)^n b) f(n) = n(3)^n