Assume x is a particular real number and use De Morgan’s laws to write negations for the statement x<2 or x>5

Write the negation of of the following statement: “For every pair of real numbers x and y if x < y, then there exists a rational number q such that x < q < y.”

Discrete Math. This question is based on predicates and quantifiers. Please show all work and identify the type of each given statement to its correct match.

For each one, state whether the statement is TRUE, FALSE. Then, state the negation:1.∃a(ais a prime number)2.∀a(ais a power of 2)3.∃a∃b(a+b <0)

4. Write the negation of the following statements. Use number lines where necessary. Define variables ifneeded.(a) Every odd integer is prime (b) I hate onions but I love sushi (c) -3 ≤ x ≤ 3

Consider the following conditional statement for a real number n: If n² is a rational number, then 2n − 1 < n². (a) Write the converse of the original statement: (b) Write the negation of the original statement: Write the contrapositive of the original statement: (d) Of (a)-(c), which is logically equivalent to the original statement? (e) Provide a value for n that makes the negation of the original statement (your answer for (b)) true and justify your answer.

In the following items determine whether the proposed negation is correct. If is is not, write a correct negation. (a) Statement: The product of any irrational number and any rational number is irrational. Proposed negation: The product of any irrational number and any rational number is rational. (b) Statement: For all real numbers ₁ and 2, if x = Proposed negation: For all real numbers ₁ and I1 = I2. then ₁ = 2₂. 2, if z then

Assume x is a particular real number and use De Morgan’s laws to write negations for these statements 1 > x ≥ −3 0 > x ≥ −7