1) For each of the following statements, (1) write the statement informally without using variables or the symbols V or 3, and (2) indicate whether the statement is true or false and briefly justify your answer. a) V integers a, 3 an integer b such that a +b= 0. b) 3 an integer a such that V integers b, a +b = 0.

What is the value of the following statement ? Let a ₁ = −2, a 2 = −1, a3 =0, a 4 = 1, and a5 = 2 1 2 -1 0 -2 2 k = 1 a 2 k

Fill out the following expression with logical operators so that it returns False as the answer. You must not add or delete any other operators and/or operands.      4.5 / 2 >= 5 - 3 _____ (3 == 1 + 2 _____ 5 * 2 < 2 * 5)

Which of the following statements are correct if yi =2xi ∀i = 1, 2, ....., n? A. y = 2x B. y = 4x C. s2y = 2s2x D. s2y = s2x + 4

Express this in predicate logic: Each email address has exactly one email box. M(x): x is an email address B(x,y): x has an email box y

For each of the statements below, write its converse and its contrapositive. (a) If A \ B = A, then AnB = 0. Converse: Contrapositive: (b) If P(A) CP(B) and BCC, then P(A) ≤ P(C). Converse: Contrapositive:

Paraphrase the following into quantificational notation: (a) If any student taking Logic cheats, then every student taking Logic will be unhappy. (b) If any student taking Logic cheats, then he or she will be unhappy. (c) Logic students are either clever or happy. (d) If anything is both gaseous and liquid, then it is a plasma. (e) No plasma is a liquid unless some plasma is a gas.

I want written justification along.

Please answer the following questions.

Determine whether the following statement is true or false. The product of two negative real numbers is positive. Choose the correct answer below. O A. True, because the product of two real numbers is always positive. O B. False, because the product of two negative real numbers is zero. O C. False, because the product of two negative real numbers is negative. O D. True, because the product of two real numbers with the same sign is always positive.