Discrete Mathematics Answers

Answer the following:

(a) You have a standard 52 card deck. If you draw two cards at random, what is the probability that they are both hearts?

(b) You reshuffle your cards into the deck, but unfortunately now a mischievous dog (a golden retriever named Bubbles), decides to eat one of the cards! Assuming that the missing card is a diamond, now when you draw two cards at random what is the probability that they are both hearts?

Using Binomial Theorem, give the closed form expression for: "\\textstyle\\sum_{k=0}^n""{n \\choose k}"3ⁿ · 2^k

in a class of final year student in a school, 350 offer chemistry and 200 offer physics. if 90 student offer neither chemistry nor physics;

i: how many students are offering both subject.

ii: how many students are offering only one subject.

iii: how many students are offering at least one subject

For this arguments, explain which rules of inference are used for each step. Same body in this class enjoys whole watching. Every person who enjoys whole watching cares about ocean pollution. Therefore, there is a person in this class who cares about ocean pollution.

Consider the sets A and B, where A = {3, |B|} and B = {1, |A|, |B|}. What are the sets?

1. ∅ ⊆ A (true or false) 2.n(∅) = 0 (true or false)

1. Represent the following sets in tabular or listing form:

(i) A={x:x^2 - 3x + 2 = 0}

(ii) B= { x:x is an integer and 1 < x < 7}

Consider the following two arguments:

A. If Fred wanted me fired then he would go to the boss. Fred is going to the boss. Therefore Fred wants to get me fired.

B. Max is a cat or Max is a mammal. Max is a cat. Therefore Max is not a mammal.

Which of the following is true?

 Find (showing your reasoning) a formula for the term tn of the sequence defined by t1 = 4; tn = 2tn−1, n ≥ 2.

[{1,2,3,4,5}, <=], Draw its Hasse Diagram.