259 Answered Questions for the topic discrete mathematics

Discrete Mathematics Math Discrete Math Linear Algebra

7d

Prove or disprove: A^2 - B^2 = (A - B)(A + B) for all square matrices A and B of the same size.

Prove or disprove: A2 - B2 = (A - B)(A + B) for all square matrices A and B of the same size.
Discrete Mathematics Calculus Discrete Math Calc

8d

Summations that are functions of n

How do I calculate this with i being n/4 nf(n) = ∑ (i) i=n/4
Discrete Mathematics Calculus Discrete Math Calc

8d

Summations that are functions of n

I can't figure out how to compute the closed-form sum for this, I'm not sure which rule applies to this, and with i not at 1 or 0. log(n)f(n) = ∑ (5n) i=3
Discrete Mathematics Math Discrete Math Mathematica

21d

Validity of the conclusion using logic rules

a) u V wb) ~wc) q →sd) u → ~pe) ~p → (r ^ ~s)∴ ~q
Discrete Mathematics Math Discrete Math Mathematica

21d

Two column proof and logic laws

((~d V e) ^ (~d V ~e)) -> f ≡ d V f
Discrete Mathematics Math Discrete Math Mathematica

21d

Validity of the conclusion using logic rules

a) u V wb) ~wc) q →sd) u → ~pe) ~p → (r ^ ~s)∴ ~q
Discrete Mathematics Math Discrete Math Mathematica

21d

Two column proof and logic laws

((~d V e) ^ (~d V ~e)) -> f ≡ d V f
Discrete Mathematics Discrete Math

25d

Use laws of logical equivalence to simplify the circuit. Justify each step. ((𝑃 ∧ ~𝑄) ∨ (𝑃 ∧ 𝑄)) ∧ Q

Use laws of logical equivalence to simplify the circuit. Justify each step. ((𝑃 ∧ ~𝑄) ∨ (𝑃 ∧ 𝑄)) ∧ Q
Discrete Mathematics Discrete Math

25d

Write the statements formally using quantifiers and variables. Make them conditional.

Write the statements formally using quantifiers and variables. Make them conditional. a) A sufficient condition for an integer to be divisible by 8 is that it be divisible by 16. b) If a product... more
Discrete Mathematics Math Discrete Math

02/04/21

If A is a countable set, how can i show that A has countably many finite subsets?

Lets say that A is a countable set. How would I go about showing that A has countably many finite subsets? I need to show that for every n ∈ N, the set Pn(A) of finite subsets - with exactly n... more
Discrete Mathematics Discrete Math

01/26/21

Use laws of logical equivalence to verify the logical equivalence for the statements

Use laws of logical equivalence to verify the logical equivalence for the statements. (do not use truth tables!) Justify each step:𝑝 → 𝑞 ∨ 𝑟 ≡ 𝑝 ∧ ~𝑞 → rPlease show me every step and explain it so... more
Discrete Mathematics Discrete Math

01/26/21

negation of the following compounded statement:

Write the negation of the following compounded statement: 𝑥 ≤ 20 or 𝑥 > 30 (where 𝑥 is some real number). −1 < 𝑥 ≤ 9
Discrete Mathematics Discrete Math

01/22/21

Find the truth value of the statement

Determine the truth-values of the following statements. Explain your reason.a) The product 6 ∗ 5 = 25 or 6 is odd b) If we are in the month of January then 3+9 =12 c) 5 is a letter iff T is a vowel
Discrete Mathematics Discrete Math Computer Science

01/19/21

what is the original message (number)encrypted using the RSA system with n= 77 and e = 43 if the encrypted message is 0202

what is the original message (number)encrypted using the RSA system with n= 77 and e = 43 if the encrypted message is 0202...............................need solution with explinations
Discrete Mathematics Math Computer Calculus

12/24/20

Suppose that a person deposits 10.000 dollars in a savings account at a bank yielding % 11 per year

Suppose that a person deposits 10.000 dollars in a savings account at a bankyielding % 11 per year with interest compounded annually. How much will bein the account after 10 years, 20 years, 30 years? more

12/23/20

DISCRETE MATHEMATICS

Let p, q, and r be propositions.(a) Use logical equivalences (De Morgan’s laws, etc.) to show that¬(p ∨ (¬p ∧ q)) ≡ ¬p ∧ ¬q.(b) Show that (p ⇒ r) ∨ (q ⇒ r) ≡ (p ∧ q)) ⇒ r (use any method you like).
Discrete Mathematics Discrete Math

12/22/20

Discrete Mathematics

Conjecture a simple formula for an if the first terms of the sequence an are 1,7, 25, 79, 241, 727, 2185, 6559, 19681, 59047.
Discrete Mathematics Discrete Math

12/22/20

Discrete Mathematics

Suppose that a person deposits 10.000 dollars in a savings account at a bank yielding % 11 per year with interest compounded annually. How much will be in the account after 10 years, 20 years, 30... more
Discrete Mathematics Discrete Math

12/22/20

Discrete Mathematics

Let p, q, and r be propositions.(a) Use logical equivalences (De Morgan's laws, etc.) to show that ¬(p ∨ (¬p ٨q)) ≡ ¬p ٨ ¬q.(b) Show that (p ⇒ r) ∨ (q ⇒ r) ≡ (p ٨ q)) ⇒ r (use any method you like).

12/22/20

Discrete Mathematics

Determine the truth values of each proposition below.(a) 1 + 1 = 3 if and only if 2 + 2 = 3.(b) If 1 + 1 = 2 or 1 + 1 = 3, then 2 + 2 = 3 and 2 + 2 = 4.(c) If squirrels play badminton, then cats... more
Discrete Mathematics Math Discrete Math Computer Science

12/22/20

Discrete Mathematics

Let p, q, and r be the propositions.p : Grizzly bears have been seen in the area,q : Hiking is safe on the trail,r : Berries are ripe along the trail.Write the following propositions using p, q,... more
Discrete Mathematics Math Discrete Math Computer Science

12/22/20

Discrete Mathematics

Let p and q be the propositions "Swimming at the Sariyer shore is al- lowed" and "Sharks have been spotted near the shore", respectively.Express each of these compound propositions as an English... more
Discrete Mathematics Math Discrete Math Computer Science

12/22/20

Discrete Mathematics

Is the assertion "This statement is false." a proposition? Justify.

12/20/20

Discrete Mathematics

Let A and B be subsets of the set S, where S = 10 and B = 5. Let f: A → Bbe a function.(a) If f is one-to-one, what are the possible values of A?(b) If f is onto, what are the possible values of... more

12/20/20

Discrete Mathematics

Let B be a subset of A. Let A = n and B = k. What is the number ofsubsets of A whose intersection with B has 3 elements?

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