Discrete Mathematics Answers

1. Find the product of 10101₂ and 101₂. 

Show ALL working.

Determine whether ( 𝑝∨𝑞)∧(𝑝→𝑟)∧( 𝑞→𝑠)→𝑟∨𝑠 is a Tautology or a contradiction using a truth table

Give full truth table

Prove for every integer n, n4 has the form 8m or 8m + 1 for some integer m. Hint: Use 2 cases.

Convert the following formula to conjunctive normal form: A ⇒ ( B ∧ C )

A. ( ¬A ∨ B ) ∧ ( ¬A ∨ C )

B. ( A ∧ ¬B ) ∨ ( A ∧ ¬C )

C. ( ¬A ∧ B ) ∨ ( ¬A ∧ C )

D. ( A ∨ ¬B ) ∧ ( A ∨

The population of City A is 8,000,000 at the end of the year 2020.The

number of immigrants is 25,000n at the end of year n. The population

of city increases at the rate of 8% per year. Use recurrence relation to

determine the population of the city at the end of 2030.

Suppose that A, B, and C are sets such that A ⊆ B and B ⊆ C. Show that A ⊆ C.

Use a Venn diagram to illustrate the set of all months of the year whose names do not contain the letter Y in the

set of all months of the year.

show that p ↔ q and (p^q) v (¬p ^ ¬q) are logically equivalent.

Use a Venn diagram to illustrate the subset of even integers in the set of all positive integers not exceeding 15. 

Let R1 and R2 be two relation on real number such that R1 = {(x, y)|x < y} and R2 =

{(x, y)|x > y}, then find R1 ∪ R2,R1 ∩ R2,R1 − R2, R2 − R1, and R1

LR2.