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i. Domain of f
ii. Range of f
iii. G(g(g(g(7)))) if g (n) = f(209, n).
i. A intersection ii.( B intersection C ) complement iii. A complent union C complent iv. B complent union C complent
Let set A = {1, 2, 3, 4} and B = {5, 6, 7, 8} whereby relation R1 = {(a, b) | a = b - 1 } and R2 = {(a, b) | a + b ≥ 3}. a is an element of set A and b is an element of set B.
- Write the relation for R1 and R2 where these represent the relation from set A to set B.
- Based on question in (1), solve R1 – R2 and R2 – R1
Let p, q and r be the propositions
p : Grizzly bears have been seen in the area.
q : Hiking is safe on the trail.
r : Berries are ripe along the trail.
Write these propositions using p, q, and r and logical connectives (including negations).
(a) Berries are ripe along the trail, but grizzly bears have not been seen in the area.
(b) Grizzly bears have not been seen in the area and hiking on the trail is safe, but berries
are ripe along the trail.
(c) If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not been
seen in the area.
(d) It is not safe to hike on the trail, but grizzly bears have not been seen in the area and
the berries along the trail are ripe.
(e) For hiking on the trail to be safe, it is necessary but not sufficient that berries not be
ripe along the trail and for grizzly bears not to have been seen in the area.
(f) Hiking is not safe on the trail whenever grizzly bears have been seen in the area and
berries are ripe along the trail.
Employ the Gauss-Seidel method, solve the system. 10𝑥 + 𝑦 + 𝑧 = 12 2𝑥 + 2𝑦 + 10𝑧 = 14 2𝑥 + 10𝑦 + z=13
Determine all eigenvalues and the corresponding eigenspaces for the matrix 𝐴 = [ −9 4 4 −8 3 4 −16 8 7 ]
Determine whether each of these functions is a bijection from R to R.
f (x) = (x2 + 1)/(x2 + 2)
Let X = {a, b, c} defined by f : X X such that f = {(a, b), (b, a), (c,c)}. Find the values of
f–1, f2 and f4.
b) Let L = {3, 4, 12, 24, 48, 82} and the relation < be defined on L such that x < y if x divides y. Draw the Hasse diagram.
c) Show that the functions, defined by : are inverse of one another
#339914 on Dec 2023