product of and D. While A × (B × C) × D is the Cartesian product of A and the Cartesian product of B
and C and finally the Cartesian product of D.
In more simple terms, (A × B) × (C × D) is (a,b) x (c,d) while A × (B × C) × is (a) x (b,c) x (c)
42)
a) There exists some x in the domain of reals such that x^3 = -1. This is true because x = -1
b) There exists some x in the domain of integers such that x+1>x. This is true because x = 1
c) For all x in the domain of integers, x- 1 is contained in the domain of integers. This is true
because any integer minus 1 (another integer) is still an integer.
d) For all x in the domain of integers, x^2 is contained in the domain of integers. This is true
because any integer squared (times itself) is still an integer.
2.2
2)

a) A∩B
b) A- B
c) A
∪
B
d) A’
∪
B’
4)
a) {a,b,c,d,e,f,g,h}
b) {a,b,c,d,e}
c) { }
d) {f,g,h}
18)
a) From the definition of union, A
∪
B is a subset of A
∪
B
C because
∪
A
∪
B is in A
∪
B
∪
C
b) This should be false because every element of (A ∩ B ∩ C) is not in (A ∩ B)
26)
a)
b)
c)
32) {2, 4}
48)
a) {1,2,3, . .. , n}
b) {1}
50)

52)
a) 0011100000
b) 1010010001
c) 0111001110
54)
a) A subset of x that contains no x
b) A subset of x that is included each position in x

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- Summer '19