Discrete Mathematics Answers

Find, showing all working, a formula for the n-th term tn of the sequence (tn) defined by t1 = 5; tn = −7tn−1/3, n ≥ 2.

Give the power set of the following sets.

(a) /0 (b) {1} (c) {1,2} (d) {1,2,3}

. Let p and q be the propositions p: He is rich q: He is happy Write the following propositions using p and q and logical connectives.

a. If he is rich, then he is unhappy.

b. He is neither rich nor happy.

c. It is necessary to be poor, in order to be happy.

d. He is either rich or happy (or both).

Show following equivalence without considering the truth table.

(𝑝̅ ∧( 𝑞̅∧𝑟)) ∨(𝑞 ∧𝑟) ∨(𝑝 ∧𝑟)↔𝑟

Prove by contradiction that for any integer n if n² is odd then n is odd.

Write the converse, inverse, and contrapositive of the statement “If

5 is an odd number, then it is a prime number.”

Build a truth table then verify if the proposition is Tautology, Contradiction, and Contingency.

(p ↔ q ) Λ ( ┐p Λ q )    

. Which of the intervals (0, 5), (0, 5], [0, 5), [0, 5], (1, 4], [2, 3], (2, 3) contains

a) 0?

b) 1?

c) 2?

d) 3?

e) 4?

f ) 5?