Discrete Mathematics Answers

(a)   If x is nonnegative, then x is positive or x is 0. 

Create a schematic diagram of all odd numbers from 20 to 45

If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not been seen in the area.

Which of the following functions are injective? Which are surjective?

a) f: Z → Z given by f(x) = x² + 1.

b) g: N → N given by g(x) = 2^x.

c) h: R → R given by h(x) = 5x - 1.

Let f be the function from x ={0, 1, 2, 3, 4, 5} to X defined by

f(x) = 4x mod 6.

Write f as a set of ordered pairs and draw the arrow diagram of f . Is f one-to-one? Is f onto?

show that C(n+1,k)=C(n,k-1)+C(n,k)

Let R = {(1,4), (2,1), (2,5),(2,4),(4,3),(5,3),(3,2)} on the set A = {1, 2, 3, 4, 5}. Use Warshall’s algorithm to find transitive closure of R.

20. Determine the truth value of each statement if the domain consists of all real numbers. (4 pts.)

a) ∃𝑥(𝑥3 = −1) b) ∃𝑥(𝑥4 < 𝑥2) c) ∀𝑥((−𝑥)2 = 𝑥2) d) ∀𝑥(2𝑥 > 𝑥)

Let Q(x) be the statement “x + 1 > 2x.” If the domain consists of all integers, what are these truth values? (7 pts.)

a) 𝑄(0) b) 𝑄(−1) c) 𝑄(1)

d) ∃𝑥𝑄(𝑥) e) ∀𝑥𝑄(𝑥) f) ∃𝑥¬𝑄(𝑥) g) ∀𝑥¬𝑄(𝑥)