## 7. What is the cardinality of each of the following sets? a) { } b) { { } } c) {a, {a}, {a, {a}

Question

7. What is the cardinality of each of the following sets?

a) { }

b) { { } }

c) {a, {a}, {a, {a}} }

NOTE: I need the answer type out NOT hand written, the last person to answer this question teriibly hand wrote the answer and I could not read it.

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2 weeks 2021-09-09T14:51:14+00:00 1 Answer 0

The cardinality of set (a) is 0,

the cardinality of set (b) is 1

and

the cardinality of set (c) is 3.

Step-by-step explanation:  We are given to find the cardinality of each of the following sets :

(a) { }.

(b) { { } }.

(c) {a, {a}, {a, {a}} }.

We know that

CARDINALITY of a set is the number of elements present in the set.

(a) The given set is A = { }.

The set A is an empty set, so it does not contain any element. Hence, the cardinality of the set A is 0.

(b) The given set is B = { { } }.

The set is B is singleton set, contains only one element (that is empty set). So, the cardinality of the set B is 1.

(c) The given set is C = {a, {a}, {a, {a}} }.

The set C has three elements, a, the set {a} and the set {a, {a}}. So,  the the cardinality of set C is 3.

Thus,

the cardinality of set (a) is 0,

the cardinality of set (b) is 1

and

the cardinality of set (c) is 3.