Cardinality and Subsets

[Samin]

1.What is the cardinality of the set A = {x:x is even and 2<X<17}?
2.What is the number of all possible subsets of the set A={e,g,f}?

this is what i’ve done,correct me if i’m wrong
1.even numbers between 2-17
2,4,6,8,10,12,14,16 so cardinality = 8

2.{e} {g} {f} {eg} {gf} {ef} {egf} φ so number of subsets = 8

 

[lex]

1. x can be any even number between (not including) 2 and 17. (There is no equal sign on the inequalities, < not ≤, so x≠2, x≠17). Therefore A={4, 6, 8, 10, 12, 14, 16} and has cardinality 7.

2. As the original set A has 3 elements, the number of possible subsets is 2^3 (2 to the power of 3 is 8).
Your answer is correct.

(If there had been 5 elements it would be 2^5 etc...)
(The set of all possible subsets of A is called the Power Set of A).

For each subset, each element can be in one of 2 'states' either in the subset or not in it. That gives a total of 2 x 2 x 2 different possible subsets using 3 elements.

 

[Samin]

1. x can be any even number between (not including) 2 and 17. (There is no equal sign on the inequalities, < not ≤, so x≠2, x≠17). Therefore A={4, 6, 8, 10, 12, 14, 16} and has cardinality 7.

2. As the original set A has 3 elements, the number of possible subsets is 2^3 (2 to the power of 3 is 8).
Your answer is correct.

(If there had been 5 elements it would be 2^5 etc...)
(The set of all possible subsets of A is called the Power Set of A).

For each subset, each element can be in one of 2 'states' either in the subset or not in it. That gives a total of 2 x 2 x 2 different possible subsets using 3 elements.

Thank you ?

 

[lex]

No problem