What is the cardinality of each set?

Question

E= element in set. e = subset of set
a.){x E Z : |x| <= 10}

b.){x E Z : 1 <= x^2 <= x}

c.){x E Z : x E empty set}

d.){x E Z : empty set E x}

e.){x E Z : empty set e {x}}

f.)2^[2^{1,2,3)]

g.){x E 2^{1,2,3,4} : |x|=1}

h.){{1,2}, {3,4,5}}

Answer 1

First of all, the cardinality of Z or any infinite subset of Z
is א null, the first infinite cardinal number.
So here are the answers:
a. 21. This includes all the integers between -10 and 10.
b. 1. 1 is the only integer in this set.
c. 0. There is nothing in the empty set
d. 0, A set cannot be a member of an element
e. א null. The empty set is a subset of every set.
f. 0. This isn't a set. Also, you can't raise an
integer to a set.
g. 0. a). You can't raise an integer to a set.
b. Even if you interpret this as
{x: x E {2,4,6,8 ^ x = 1 or -1}
1 raised to any power is 1 and -1 raised to
any power is 1 or -1 so there no elements in this set.
h. 2. Both elements of this set are themselves sets.

Answer 2

a. 21
b. 1 (x = 1)

I don't get your notation for c through e. Someone is trying to test you on subtle stuff regarding the null set.

f. 2^8 = 256
g. 4 (the four sets with 1,2,3,4 in them individually)
h. 2 (there are two sets in the set)