- #1
rayne1
- 32
- 0
Let P(x) be assertion “x is prime”, E(x) be “x is even”, and D(x, y) be “x divides y” (i.e., y/x is an integer). Consider the following statement:
R = (∀x ∈ Z)(P(x) ⇒ ((∃y ∈ Z)(E(y) ∧ D(x, y))))
Write the negation of R, and determine which statement is true, R or ¬R.
I tried, but I'm not sure if I got the correct answer:
¬R = (∃x ∈ Z)(P(x) ∧ (∀y ∈ Z)((¬E(y)) ∨ (¬D(x, y)))
It seems that ¬R is true.
R = (∀x ∈ Z)(P(x) ⇒ ((∃y ∈ Z)(E(y) ∧ D(x, y))))
Write the negation of R, and determine which statement is true, R or ¬R.
I tried, but I'm not sure if I got the correct answer:
¬R = (∃x ∈ Z)(P(x) ∧ (∀y ∈ Z)((¬E(y)) ∨ (¬D(x, y)))
It seems that ¬R is true.