Discrete Mathematics Answers

2. A low pressure area implies a coming stormconverse, inverse and contra positive 

Number plates in an Arab country consist of 3 letters (chosen from a specified set of 20 letters from the Arabic alphabet) and 4 digits (from 0 to 9).

Find the probability of a plate having identical letters.

Find the probability of a plate having identical digits.

a. Determine the sets A and B, if A − B = {1, 2, 7, 8}, B − A = {3, 4, 10} and A ∩ B

= {5, 6, 9}.

b. Verify A ∪ (A ∩ B) = A using the rules of set algebra

6.

A multiple-choice test contains 10 questions. There are four possible answers for each question. b) In

how many ways can a student answer the questions on the test if the student can leave answers

blank?

The relation R on the set A={1,2,3,4,5}is defined by the rule (a,b) €R if 3|a-b|

Find a counterexample, if possible, to these universally quantified statements, where the domain

for all variables consists of all integers.

a) ∀x (x2 ≥x)

b)∀x(x>0∨x<0) c) ∀x (x = 1)

What are the truth values of these statements?

[3 marks]

a) ∃!xP(x)→∃xP(x)

b)

∀x P(x) → ∃!xP(x)

c)

∃!x¬P(x)→¬∀xP(x)