Discrete Mathematics Answers

If the domain is the set of words {violet, indigo, blue, green, yellow, orange, red}, which of the following sentences is/are true?


(P)∀x(if x does not contain the letter ‘e’, then x contains the letter ‘n’)
(Q) ∃x(if x contains the letter ‘e’, then x contains at most 4 letters)

(R) ∀x(if x contains more than 5 letters, then x contains the letter ‘o’)

P:the cow is old
Q:it is dying
Express each of these prepositions as an English sentence
p v q. p ^q. p v(~q)

Prove the following

If a is odd and b is even, then a2 – b2 is an odd number

“If it is a wild animal, then it is dangerous. If it is dangerous, then it will hurt you. However, it is
not dangerous. Therefore, it is not a wild animal.

Give a step-by-step argument using valid Rules of Inference

Give that the universal set

• µ = (1,2,3,4,5,6,7,8,9,10) , p = (1,2,4,6,10) and Q = (2,3,6,9).
Show that (P U Q)’= P’ n Q’

According to information obtained from mathematics department regarding three mathematics units done by 100 students, those who are doing calculus are 45, those doing discrete are 49 and those doing statistics are 38. Those doing calculus and discrete are 17, those doing calculus and statistics are 12 and those doing the three units are 5. Use Venn diagram to find the number of students doing discrete and statistics but not calculus

What is the value of k after the following code has been executed?
k := 0
for i1 := 1 to n1
for i2 := 1 to n2
.
.
.
for im := 1 to nm
k := k + 1

a) A market researcher investigating consumers preference for three brands of beverages namely; coffee, tea and cocoa in Thika town gathered the following information.
From a sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa, 30 took all the three beverages, 70 took coffee and cocoa, 110 took coffee only, 185 took cocoa only.
Required:
i). Present the above information in a venn diagram. [2mks]
ii). The number of consumers who took tea only. [2mks]
iii). The number of customers who took tea and cocoa only. [2mks]
iv). The number of customers who took tea and cocoa only. [2mks]
v). The number of customers who took none of the beverages. [2mks]

Show that the following argument form is valid.

p --> q
q --> r

∴ p --> r

How many 20 digit binary numbers have four 1's in them?