MAT1501 Assignment 3 2025 Due August 2025

Description

MAT1501 Assessment 3 (2025)
Question 1
(a)
A = {x ∈ R : x > −3}

is all real numbers greater than  . On a number line, draw an
−3
open circle at
−3
and shade to the right (toward
+∞ B = (−4, 5]
).
includes all   with
x
−4 < x ≤ 5
. On a number line, draw an open circle at  , a closed circle at  , and shade
−4
5
between them.
(b) By definition,
A ∪ B = { x ∣ x ∈ A or x ∈ B}
. Since   already includes all
B
x >
−4
up to  , and   includes all
5 A
x > −3
beyond, their union is all
x > −4
. In set-builder
form:
A ∪ B = { x ∈ R ∣ x > −4}.
(c) The union
A ∪ B
is the interval
(−4, ∞)
. Sketch this by an open circle at

−4
and
shading to the right without bound.
(d) By definition,
A ∩ B = {x x A and x B}
. Here   requires
A
x > −3 B
and