If P and Q are predicates over some domain, and if it is true that Vx(P(x)V Q(x)), must VxP(x) v VæQ(x) also be true? Explain.
1 answer:
Answer:
It is not true
Step-by-step explanation:
Suppose your domain is the integer numbers. Define
P(x)="x is even"
Q(x)="x is odd"
So we have that the predicate is always true because the integers are always even or odd. But the predicate
means that <em>all the integer numbers are even</em> or <em>all the integer numbers are odd</em>, which is false. So we can't deduce
from
.
You might be interested in
Step-by-step explanation:
A left Riemann sum approximates a definite integral as:
Given ∫₂⁸ cos(x²) dx:
a = 2, b = 8, and f(x) = cos(x²)
Therefore, Δx = 6/n and x = 2 + (6/n) (k − 1).
Plugging into the sum:
∑₁ⁿ cos((2 + (6/n) (k − 1))²) (6/n)
Therefore, the answer is C. Notice that answer D would be a right Riemann sum rather than a left (uses k instead of k−1).